Five days after the attack on the Capitol last year, the Republican members of the House of Representatives braced for a backlash.

Two-thirds of them — 139 in all — had been voting on Jan. 6, 2021, to dispute the Electoral College count that would seal Donald J. Trump’s defeat just as rioters determined to keep the president in power stormed the chamber. Now one lawmaker after another warned during a conference call that unless Republicans demanded accountability, voters would punish them for inflaming the mob.

“I want to know if we are going to look at how we got here, internally, within our own party and hold people responsible,” said Representative Nancy Mace of South Carolina, according to a recording of the call obtained by The New York Times.

When another member implored the party to unite behind a “clarifying message” that Mr. Trump had truly lost, Representative Kevin McCarthy of California, the Republican leader, emphatically agreed: “We have to.”

More than 20 months later, the opposite has happened. The votes to reject the election results have become a badge of honor within the party, in some cases even a requirement for advancement, as doubts about the election have come to define what it means to be a Trump Republican.

The most far-reaching of Mr. Trump’s ploys to overturn his defeat, the objections to the Electoral College results by so many House Republicans did more than any lawsuit, speech or rally to engrave in party orthodoxy the myth of a stolen election. Their actions that day legitimized Mr. Trump’s refusal to concede, gave new life to his claims of conspiracy and fraud and lent institutional weight to doubts about the central ritual of American democracy.

Yet the riot engulfing the Capitol so overshadowed the debate inside that the scrutiny of that day has overlooked how Congress reached that historic vote. A reconstruction by The Times revealed more than simple rubber-stamp loyalty to a larger-than-life leader. Instead, the orchestration of the House objections was a story of shrewd salesmanship and calculated double-talk, set against a backdrop of demographic change across the country that has widened the gulf between the parties.

While most House Republicans had amplified Mr. Trump’s claims about the election in the aftermath of his loss, only the right flank of the caucus continued to loudly echo Mr. Trump’s fraud allegations in the days before Jan. 6, The Times found. More Republican lawmakers appeared to seek a way to placate Mr. Trump and his supporters without formally endorsing his extraordinary allegations. In formal statements justifying their votes, about three-quarters relied on the arguments of a low-profile Louisiana congressman, Representative Mike Johnson, the most important architect of the Electoral College objections.

On the eve of the Jan. 6 votes, he presented colleagues with what he called a “third option.” He faulted the way some states had changed voting procedures during the pandemic, saying it was unconstitutional, without supporting the outlandish claims of Mr. Trump’s most vocal supporters. His Republican critics called it a Trojan horse that allowed lawmakers to vote with the president while hiding behind a more defensible case.

Even lawmakers who had been among the noisiest “stop the steal” firebrands took refuge in Mr. Johnson’s narrow and lawyerly claims, though his nuanced argument was lost on the mob storming the Capitol, and over time it was the vision of the rioters — that a Democratic conspiracy had defrauded America — that prevailed in many Republican circles.

That has made objecting politically profitable. Republican partisans have rewarded objectors with grass-roots support, paths to higher office and campaign money. Corporate backers have reopened their coffers to lawmakers they once denounced as threats to democracy. And almost all the objectors seeking re-election are now poised to return to Congress next year, when Republicans are expected to hold a majority in the House.

Objectors are set to fill the Republican leadership posts and head a majority of the committees. All eight Republicans in the House seeking higher office voted against the Electoral College tally, while a dozen Republican lawmakers who broke with Mr. Trump have either lost primaries or chosen to retire.

Playing to Trump loyalists, many across the party have made a slogan of “election integrity” — a “dog whistle” perpetuating the erroneous belief that Mr. Trump’s victory was stolen, as one dissenting Republican put it in a party meeting. More than a third of the objectors joined a new Election Integrity Caucus, which advocates stricter voter requirements and has featured speakers who supported Mr. Trump’s efforts to fight his loss.

All the Republicans who objected say they were following an example set by Democrats who objected to Electoral College results in 1968, 2000, 2004 and 2016. In each case, Republicans accused Democrats of damaging democracy and “thwarting the will of the people,” though only small numbers of Democrats joined those objections, which all came after the losing Democratic presidential candidates had already conceded. (Mr. Trump only relinquished his claim to the White House the day after House Republicans — and rioters — failed to block the Electoral College count.)

But several Republican lawmakers argued that the scale of their vote to object would do more to encourage legislators of either party to mimic the tactic — potentially upending the peaceful transfer of executive power if an aggrieved party controls Congress.

“It is a horrible precedent,” said Representative Tom Rice, a five-term Republican representing conservative Myrtle Beach, S.C., who was the only objector to express any regrets and lost a primary this summer.

Some continue to recast their objections. Legislators in Democratic-leaning territory who once thundered about defending the republic now insist they meant only a legalistic protest against certain Covid-19 rule changes — like Representative Lee Zeldin, the Republican candidate for governor in heavily Democratic New York, who railed in a Jan. 6 floor speech about his outrage over “confirmed, evidence-filled issues” in the 2020 vote.

But many have moved the other way, more fully embracing Mr. Trump’s claims than they did in the aftermath of the riot.

Representative Markwayne Mullin of Oklahoma, a former mixed martial arts fighter, experienced the center of the maelstrom. He broke off the leg of a wooden stand as a weapon to help defend the floor of the House, then watched from a few feet away as a Capitol Police officer shot and killed one of the assailants.

Amid the wreckage of the violence, the congressman justified his objection by hewing closely to Mr. Johnson’s lawyerly nuance. But now, as the favored candidate for a Senate seat in Oklahoma, Mr. Mullin is more categorical.

Was Mr. Trump “cheated out of the election?” a moderator asked in a recent televised debate.

Mr. Mullin replied, “Absolutely.”

‘A Fig-Leaf Intellectual Argument’

The House vote to formalize presidential election results is customarily ceremonial. But in 2021 Mr. Trump changed that, demanding, like no president before, that House Republicans reject the results from several states.

On the eve of the vote, Representative Liz Cheney of Wyoming, then chairwoman of the House Republican Conference, called an unusual meeting in the congressional auditorium. Her goal was to convince her fellow Republicans that the Constitution gave Congress no role in deciding presidential elections, and in the days before the meeting, she also distributed a 21-page summary of court rulings — many by Trump-appointed judges — that found no evidence of meaningful fraud.

Representative Chip Roy, a former top official in the Texas attorney general’s office and a staunch conservative, made the same case, warning that “history will judge this moment.”

“If a majority of Republicans vote to reject the electors, it will irrevocably empower Congress to take over the selection of presidential electors,” he said, according to one of several recordings included in the audio version of “This Will Not Pass,” a book by Jonathan Martin and Alexander Burns, who covered the 2020 election for The Times.

“Doing so,” Mr. Roy continued, “will almost certainly guarantee that a Democrat House would vote to reject the electors of Texas or any of your states, based on our use of voter ID, our failure to adopt mail-in ballots, our choice of voting locations or otherwise.” He also pointed out that Republicans had just voted to seat themselves, accepting the tallies of their individual congressional races, despite their suspicions.

Others, however, reminded colleagues that their constituents overwhelmingly believed Mr. Trump had won in a landslide. “Don’t anybody fool themselves into thinking you are going to be able to make a constitutional argument at your Lincoln Day dinners,” said Representative Larry Bucshon of Indiana, according to the recording.

Mr. Johnson of Louisiana offered a third way.

Members could simply accept the results, as Ms. Cheney and Mr. Roy insisted, or they could vote to object because of the fraud concerns raised by the president and his allies. But Mr. Johnson argued that they could take a different path: object based on what he called “constitutional infirmity.”

The Constitution stipulates that state legislatures set election rules. Yet some state officials, without asking their legislatures, loosened restrictions on mail-in or early voting to deal with the pandemic. That was unconstitutional and grounds to reject the election results from those states, Mr. Johnson argued.

The notion that Congress might have a say about the authority of state legislatures was unorthodox, especially among conservatives who emphasize state autonomy. But Mr. Johnson was well cast to make the case, telling colleagues he had studied up on the electoral issue — “more than when I first became a constitutional lawyer 20 years ago,” according to a previously unreported portion of the recording.

A boyish-looking 50-year-old with dimpled cheeks and rimless glasses, he had made his name as a litigator for the Alliance Defending Freedom, a conservative counterweight to the American Civil Liberties Union. When Louisiana was defending its ban on same-sex marriage, Mr. Johnson twice argued its case at the state Supreme Court.

His connections on the right helped him leapfrog in his second term to head of the Republican Study Committee, a caucus that disseminates conservative policy research to nearly 160 members.

Combining hard-line views with a gentle style has been his hallmark. To show support for racial equality, he has told audiences that he and his wife adopted a Black teenager they met through an evangelical youth group — like the movie “The Blind Side” but without the N.F.L. prospects, he has quipped.

He once shared the story with a mostly Democratic audience at a congressional hearing on slavery reparations, and he was surprised to hear boos as he spoke, he later recounted to the Council for National Policy, an assembly of conservative donors known for its strict secrecy. “I had my feelings surgically removed back in the ’80s,” he joked, according to a recording of the event, and then suggested the hearing had been packed with Black Panthers who disapproved of the mixing of races. (The Black Panther Party dissolved decades ago, and the jeers appeared to come at other moments in his remarks.)

During Mr. Trump’s first impeachment — for trying to squeeze favors from Ukraine — Mr. Johnson defended the president on television so energetically that he was invited to join his defense team. And on Nov. 8, 2020, the day after Joseph R. Biden Jr. gave a victory speech, the president called again, “wanting to vent,” Mr. Johnson said in an interview with The Times. “‘We have been cheated’ and all that — and he believes that to his core today.”

Mr. Johnson’s public statements suggest that he initially agreed.

“There is still reason for hope” that Mr. Trump might win, he told a conservative Louisiana talk radio host a week after the election, citing “credible allegations of fraud and irregularity.” Charges that voting machines had been “rigged” had “a lot of merit,” he asserted in another radio interview.

“When the president says the election is rigged, that’s what he’s talking about — that the fix was in,” Mr. Johnson added.

Some of his closest political allies — especially Representative Jim Jordan of Ohio, a relationship Mr. Johnson has described as “like Batman and Robin” — kept up the cheating claims even after courts and Mr. Trump’s attorney general had debunked them.

“There was fraud on top of the unconstitutional way they ran the election,” Mr. Jordan declared on Fox Business on Jan. 5, 2021.

Yet Mr. Johnson now says he never bought the claims of massive fraud. “I never egged on any of that,” he said. “I never was in that other camp, anytime, ever.”

“I was like a lone wolf crying in the wilderness: ‘Guys, you don’t have to worry about any of that,’” he said in the interview. “‘They violated the Constitution!’”

Democrats, seeing an advantage, have long pushed for easier balloting just as Republicans have favored tighter regulations. Still, even if state officials loosened the rules “in good faith” but did not receive the required legislative approval, Mr. Johnson said, “it’s the ‘fruit of the poisonous tree’ doctrine: If the process is broken, it cannot produce good fruit, as unpopular as that may be.”

“If you are convinced the Constitution was violated in the process, I am not sure how the set of electors could then be deemed acceptable,” he added, noting that the Supreme Court has agreed to hear a case on the relative power of state legislatures and courts over elections rules.

Many legal experts sympathetic to his argument still say Congress does not have authority to rule on the constitutionality of a state’s election procedures, especially after voters have cast ballots. What’s more, the total number of ballots affected by pandemic rule changes would not have undone the results in Pennsylvania and other contested states.

Even so, in early December 2020, the Texas attorney general filed a long-shot appeal citing an array of unproven claims of fraud and other irregularities and asking the U.S. Supreme Court to invalidate the Pennsylvania results on similar constitutional grounds.

Mr. Johnson drafted a supporting brief that focused on the constitutional argument. As chairman of the Republican Study Committee, he pushed its members to sign the brief, and he also wrote an email to all Republican lawmakers warning in bold red letters that Mr. Trump would be tracking their response. “He said he will be anxiously awaiting the final list to review,” he wrote.

The lawyer for the House Republican leadership told Mr. Johnson that his arguments were unconstitutional, according to three people involved in the conversations, and Ms. Cheney, also a lawyer, called the brief “embarrassing.” Mr. McCarthy, the Republican leader, told members that he refused to sign, the three people said.

Nonetheless, Mr. Johnson pushed ahead and filed the brief on Dec. 10 with 105 lawmakers as co-signers, and within a day he had added 20 more — including Mr. McCarthy. Later, at the caucus meeting on Jan. 5, 2021, Mr. Johnson suggested the signers, in effect, had signaled their support for declaring “constitutional infirmity” as grounds for objecting. Most of the signers did exactly that.

Ms. Cheney, through a spokesman, declined to comment. But three colleagues said she had called Mr. Johnson’s role “extraordinarily destructive,” noting that his image as an ultraconservative constitutional lawyer had convinced members who would never have followed outliers like Representative Lauren Boebert of Colorado or Representative Marjorie Taylor Greene of Georgia.

“It was a fig-leaf intellectual argument,” Representative Peter Meijer, a Michigan Republican who voted to impeach the president and then lost a primary this summer, said of the procedural justification.

“But that was what a lot of the objectors who were trying to make a plausible argument were hanging their hat on,” he added, noting that within the chamber “very few” were still arguing by then that the election was stolen.

‘The Heart and Soul of America’

South Carolinians demanding that Mr. Rice object to the election results had been jamming the phones at his congressional office for weeks, and one day in the lead-up to the Jan. 6 vote he answered a call himself.

“She just lit into me for 30 minutes about how there were truckloads of absentee ballots, unsigned, that were accepted — all these allegations you read in QAnon,” Mr. Rice said in an interview. “It was very, very high-intensity at that time.”

A former Myrtle Beach tax lawyer and accountant, Mr. Rice, 65, had been elected to local office with the Tea Party wave in 2010 and to Congress two years later. At a Trump campaign event, he called the 2020 election “a battle for the heart and soul of America,” predicted that Democrats would not “play fair” and urged Republicans to get out every vote. He carried the district by 24 points, even besting Mr. Trump’s margin.

Mr. Rice is a typical objector in many ways. They are disproportionately white, male and Christian, whether compared with the general public or with Congress as a whole. Out of the 139 House lawmakers, 17 are women, seven Black or Latino and two Jewish. (Three have died since they cast their votes, and one has resigned from Congress.)

Because of partisan gerrymandering and a decades-long sorting of Americans into like-minded communities — North or South, urban or rural — all but a half-dozen objectors represent districts so solidly Republican that a primary challenge is the only meaningful electoral contest they may face, even though more than one-third come from blue or battleground states.

Like other members of Congress, many pursued professional careers before moving to Capitol Hill — as accountants, lawyers, doctors, dentists. Three dozen have military experience, and more than half hold an advanced degree, including three with Ph.D.s (in animal nutrition, British history and public policy). About 18 — Ms. Boebert and Mr. Mullin among them — never earned a traditional four-year degree, according to their congressional bios.

Following the pattern of the larger Republican caucus, about half were first elected on Mr. Trump’s coattails. About a third had not held prior elected office. Though some, like Mr. Rice, reside in cities, they often live in more rural locations.

Many represent districts where racial and demographic change is churning more swiftly than in other Republican areas. Compared with the national average, their districts have a higher percentage of white people, with lower household incomes and levels of education. But in comparison with other Republicans, the objectors represent districts where the white portion of the population is decreasing faster relative to other racial or ethnic groups, according to a Times analysis of Census data from over the past two decades. Of the 10 Republicans representing districts with the steepest relative declines in the white population, eight were objectors.

Some scholars argue that race helped drive the dispute over the 2020 election. “The best predictor of Republicans hating Democrats is the level of racial resentment,” said Lilliana Mason, a professor at Johns Hopkins University who studies polarization and public opinion.

Her research, she said, shows that as the two parties have become more identified with race, animosity between them has increased sharply, with about 70 percent of people in each of the parties now calling their counterparts a threat to the country and about 60 percent calling them “evil.”

Some Democrats have said they see racial bias in Mr. Trump’s claims of widespread election fraud in cities like Atlanta, Detroit and Philadelphia, where there are high concentrations of Black voters. But Representative Byron Donalds of Florida, one of the two Black objectors, described such suggestions as “ignorant” and meant to “gaslight voters, as opposed to having a legitimate conversation on the merits.”

Among other things, Mr. Trump and his allies have claimed that allowing people to vote early and easing access to mail-in ballots enabled fraud. “Any time you increase and you use the mail system, in this country, for voting, it’s going to be rife with fraud,” said Representative Troy Nehls of Texas.

Even so, The Times found, most of the objectors with publicly available voting records took advantage of absentee or early voting provisions when they cast their ballots in the 2020 election. Mr. Nehls was among them. All four objectors from Arizona — some of the most outspoken advocates for the debunked fraud claims — capitalized on the state’s long-established early voting rule, which the Arizona Republican Party has unsuccessfully sought to dismantle. Mr. Rice also cast an absentee ballot.

In an interview, he said he had listened with concern when Sidney Powell, one of Mr. Trump’s lawyers, promised a titanic onslaught of lawsuits about a big tech conspiracy to hide his “landslide” victory. Mr. Rice was convinced otherwise, however, when Attorney General William P. Barr said about two weeks later that he had found no evidence of significant fraud.

“Republican members of Congress wanted to believe that the Republican president was not lying to them,” Mr. Rice said. Ms. Powell, he said, was a “crackpot.”

Still, as phones in his office rang nonstop with calls from constituents demanding that he object, Mr. Rice was drawn to Mr. Johnson’s solution. Legislative authority over elections was “a legitimate constitutional issue,” Mr. Rice concluded. “Mike is the one who brought that to my attention.”

‘Covering Your Butt’

“The things we do for the Orange Jesus,” one lawmaker muttered in the Republican cloakroom on the morning of Jan. 6 as he signed hastily drafted petitions objecting to electors from a half-dozen states.

One Republican who heard the remark — a derisive reference to Mr. Trump — said it had been made by Representative Mark E. Green of Tennessee, but a spokeswoman for Mr. Green said he had heard another lawmaker say it.

“Anyone could’ve said it,” the spokeswoman wrote in an email.

In the weeks before Jan. 6, the vast majority of objectors had publicly sympathized with Mr. Trump’s allegations of conspiracy and fraud. Yet when it came time to stake out an official justification for their votes, about three-quarters chiefly relied on Mr. Johnson’s argument, including 35 who signed a statement that he had written and read aloud at the previous day’s meeting.

Representative John Rutherford of Florida had described “serious allegations of election fraud” and even urged Republican state legislatures to decertify their Biden electors. But after the violence on Jan. 6, he said he was objecting to make clear his view on state legislatures’ role in setting election rules.

“It was abundantly clear that former Vice President Joe Biden earned the 270 votes” needed to win the Electoral College, he said in a statement at the time.

In the end, even some “stop the steal” ringleaders adopted Mr. Johnson’s approach. One of them, Representative Brian Babin of Texas, had joined a conference call with Mr. Trump four days earlier and posted on social media that “those who aren’t with us are against us,” adding: “History will be unforgiving. #StopTheSteal.”

Others included Representative Ronny Jackson, a former White House doctor who had written days earlier in a Texas newspaper that “the fraud that took place on Election Day cannot be allowed to stand,” as well as Representative Andy Biggs of Arizona, who had asked legislators in his home state to decertify Biden electors.

Mr. Mullin, who is now running in Oklahoma for Senate, had called Mr. Biden “illegitimate,” posted more than a dozen messages on Twitter stoking stolen-election suspicions and, during a Fox News appearance, made spurious claims about impossibly large numbers of Democrats voting in Arizona and unreliable voting machines in Michigan.

During a telephone town hall meeting with 6,700 constituents on Jan. 4, he said Democratic control of Congress would make overturning the election results “highly unlikely” but insisted “this fight is worth fighting — that’s why we have decided we are going to contest the electoral votes.”

Yet by Jan. 6, Mr. Mullin complained only of pandemic-related rule changes.

“That’s called covering your butt,” said former Senator Barbara Boxer, a California Democrat who had backed the Democrats’ objections in 2004. “They wanted to be part of the Trump coup, but they wanted a different reason they could sell to the public.”

Mr. Johnson, in an interview, acknowledged that some lawmakers may have found his approach politically convenient.

“I am sure it was,” he said, “but as God is my witness, that was not my objective.” He never had any intent to “overturn” the election, he said. “If Trump had won, I would have had the same concerns.”

The ‘Sedition Caucus’

Mr. Mullin first overheard chatter on the earpieces of the Capitol Police. Then he saw lawmakers staring at alerts on their phones.

Moments later, shortly after 2 p.m., rioters crashed toward the House chamber. Mr. Mullin, armed with the leg of a hand sanitizer station, rushed to help secure the doors. The shattering of glass sounded like gunfire, he later recalled, and the police officers around him shouted “shots fired” as they drew their weapons.

“Is it worth it? You almost got killed!” Mr. Mullin recalled yelling at the intruders. Then an officer fatally shot one of them, Ashli Babbitt, who was trying to breach a barricaded door.

“Sir, you did what you had to do,” Mr. Mullin told the distraught officer, hugging him.

In a television interview months later, Mr. Mullin faulted Republicans, Democrats and the news media, as well as the Trump administration, for using inflammatory language that too easily “turns into anger.”

“All of us are to blame,” he said.

But just hours after his close-up view of the assault, Mr. Mullin threw his political weight behind the attackers’ cause by voting against the Electoral College results.

Representative Bill Pascrell, Democrat of New Jersey, branded the Republicans the “sedition caucus” and accused them of trying to “burn down democracy.” A few rattled senators backed off their plans to support the objections after the violence.

Mr. Rice said he almost changed his mind about objecting. “If a president can send a mob down there to intimidate Congress into doing his bidding, then we might as well not have a Congress,” he said in an interview. “We might as well have a king.”

But he ultimately pressed on with the other House objectors.

In a two-page memorandum of talking points Mr. Johnson wrote after the riot to buck up his fellow lawmakers under fire for objecting, he lamented that the violence had almost eclipsed his careful arguments.

“Most of the country has also never heard the principled reason,” he wrote.

‘Moneymaking Machines’

Key industry donors and trade groups pledged to blackball the objectors in the aftermath of the violence.

Calling the riot an “armed insurrection,” the Real Estate Roundtable said its members were appalled by lawmakers “who continue to fuel baseless claims of election fraud by refusing to certify the clear results of last November’s election.” Comcast said it was suspending contributions to objectors because “the peaceful transition of power is a foundation of America’s democracy.” Toyota described the attack as “horrific” and six months later, in the interest of “promoting actions that further our democracy,” said it would also suspend donations to objectors.

Of the 100 largest publicly traded companies in the United States, half pledged to cut off those lawmakers, according to Accountable.US, a liberal group that created a website using campaign finance reports to track the money.

But the boycotts were short-lived.

At least 33 of those 50 companies have now resumed donating to objectors, the group found. Among them are AT&T, Comcast and Toyota. The Roundtable has also given to objectors.

As of September, Fortune 500 companies and trade groups have contributed more than $27 million to the re-election campaigns of objectors, according to Accountable.US.

None of it has surprised Representative Tim Burchett of Tennessee, one of the recipients of the corporate giving.

“I figured around election time, they’re going to come back around,” he said, “and they have.”

Small donors never abandoned the objectors’ cause. Mr. Trump’s political committees raised more than a quarter-billion dollars in political donations on the pretext of contesting the election, and he has funneled $5,000 contributions, the maximum allowed, to about 100 Republican congressional incumbents, most of them objectors.

His committees also gave $1 million to the Conservative Partnership Institute, an advocacy group led in part by his former chief of staff. It hosted at least 20 objectors last winter at the Ritz-Carlton on Amelia Island, Fla., where Cleta Mitchell, a lawyer who had played a central role in Mr. Trump’s efforts to reverse the 2020 election, hosted a panel discussion. She now leads the institute’s Election Integrity Network, which pushes for tighter voter registration requirements and continues to deny Mr. Trump’s defeat.

“The election was rigged. Trump won,” the network posted to Twitter as recently as this summer.

“Election integrity” has become central to Republican solicitations for all sorts of issues, from inflation to immigration, because “if you don’t check that box, you are not relevant,” said David Ferguson, a Republican consultant who works in online advocacy. “And if you voted to certify, that is a negative.”

The phrase is “coded language,” said Denver Riggleman, a former Republican congressman from Virginia who has worked with the special House committee investigating the riot. “You’re implying the election was stolen.”

In a statement to The Times, the co-founder of the party’s Election Integrity Caucus, Representative Claudia Tenney of New York, said her group sought “to restore people’s faith in the democratic process.”

Taking a cue from Mr. Trump, several objectors have sought to raise campaign money to fight alleged election fraud. Representative Guy Reschenthaler of Pennsylvania, whose justification for objecting was solely procedural, issued an online fund-raising appeal on the anniversary of the riot: “Will you help me stop the Left from stealing our elections?”

Objectors dominate lists of the most successful campaign committee fund-raisers. High-profile newcomers like Ms. Boebert and Ms. Greene are “moneymaking machines,” Mr. Ferguson said, “because their message is what the grass roots really believed.”

In a sign of how central they have become to the right, objectors make up virtually all the incumbents backed this year by the advocacy group Club for Growth, a titan of conservative campaign money. The group has reported spending more than $17 million directly backing objectors and a similar sum attacking their opponents.

Along with smaller sums spent on other objectors, the group’s political action committee spent more than $7 million to back Representative Ted Budd in his North Carolina Senate race and $4 million on an unsuccessful Senate bid by Representative Mo Brooks of Alabama. At the rally on the day of the Capitol riot, Mr. Brooks had urged “American patriots” to “start taking down names and kicking ass.” He lost his primary to an opponent who also claimed that possible election fraud in 2020 needed further investigation.

In newly drawn districts pitting incumbent Republicans against one another in this year’s primaries, the club spent $2.1 million helping two objectors — Representatives Mary Miller of Illinois and Alex Mooney of West Virginia — beat opponents who defied Mr. Trump and voted to certify the election.

Asked about the spending, a spokesman said the group backed candidates who promoted limited-government policies, regardless of their position on the 2020 election.

In a statement to The Times, the Club for Growth’s president, David McIntosh, said, “Every Republican except Cheney and Romney has taken issue with the last election,” referring to Ms. Cheney and Senator Mitt Romney of Utah, another critic of Mr. Trump.

‘Trump-Tough’

Mr. Rice, alone among the objectors, voted to impeach Mr. Trump for inciting the riot. Sitting in his Capitol Hill office with a reporter, Mr. Rice played a video on an iPad to explain his whipping by a primary challenger who had agreed with him on almost every policy question but faulted him for betraying the former president.

The video was taken four months after Mr. Biden’s inauguration, recorded at a Myrtle Beach country club where Mr. Rice is a member and has often raised money. It shows L. Lin Wood, a high-profile champion of Mr. Trump’s fraud claims, addressing a Republican’s women’s group.

“Donald J. Trump has never conceded, has he? Because he won the election!” Mr. Wood exclaims to loud cheers and applause. “Donald J. Trump is still the guy the military will call for the code if they need a first strike.”

Exasperated, Mr. Rice put down the iPad. “Listen to what this moron says. This is what I was running against!” He described gasps of disbelief at a campaign stop at the same country club when he matter-of-factly declared that Mr. Trump had lost the election. “It was painful.”

In July, he lost this primary after receiving less than a quarter of the vote. In the 2020 general election, he had coasted to victory with 62 percent.

In an interview, Mr. Meijer, who had also voted to impeach and lost his primary, said he was surprised Republicans had not suffered a backlash from voters over the objections and the Jan. 6 riot. He argued that the leftward-tilt of the Biden administration had pushed voters back toward Mr. Trump, citing executive orders that stretched the authority of the White House to impose vaccine mandates, an eviction moratorium and the cancellation of student debt.

“These massive uses of executive power,” he said, “make people feel like, if you are not with us pushing on the brake pedal, then you are de facto helping the Democratic majority push on the gas.”

Objectors who doubled down have thrived.

Mr. Budd of North Carolina signaled support for Mr. Trump’s fraud claims in the weeks after the election by introducing the Combat Voter Fraud Act. As a Republican candidate for the Senate, he warmed up a Trump rally this spring by accusing Democrats of opposing “election integrity” because “they know they can’t win elections on a woke left agenda.” (A spokesman for Mr. Budd said he had started pushing for tighter voter registration requirements long before the 2020 election, noting the experience of a major election fraud scandal in his state in 2018.)

In Oklahoma, Mr. Mullin stood out from the pack of Republican Senate candidates by introducing a bill to officially expunge Mr. Trump’s second impeachment. It faulted the Democratic impeachment leaders for failing to note the “unusual voting patterns” and “voting anomalies of the 2020 presidential election,” or to understand why Republicans doubted that Mr. Trump had “not won re-election.” The resolution, co-sponsored by more than 30 lawmakers, did not advance, but it curried favor with the former president. In July, Mr. Trump officially endorsed Mr. Mullin.

Mr. Mullin, who owns a ranch, spent a hot Saturday that same month campaigning among his fellow cattlemen at their annual conference in Norman, Okla. One attendee, Joel Reimer, applauded him for taking a stand against the Electoral College count knowing he would be ridiculed by many for buying into conspiracy theories. Mr. Reimer, who manages a beef ranch, added, “From a small-town guy’s perspective, I personally had questions about the validity of the vote.”

The campaign gave out fliers declaring that “no one in Congress has worked harder to SAVE AMERICA” and proclaiming Mr. Mullin “TRUMP-TOUGH.” At the top of a checklist of priorities was the party’s new refrain: “Secure our elections.”

Reporting was contributed by Amudalat Ajasa, Michael H. Keller, Aimee Ortiz, Rachel Shorey and Julie Tate. Produced by Sean Catangui and Hang Do Thi Duc.

The Times drew on data from various sources to analyze the 139 objectors, including from the A-Mark Foundation, Ballotpedia, CQ, The Cook Political Report, Daily Kos, L2 and LegiStorm. Data analysis was also contributed by Andrew Beveridge and Susan Weber of SocialExplorer.com.