As Representative Mary Miller embarked on her first congressional campaign, she described herself in salt-of-the-earth, all-American terms: a mother, grandmother and farmer who embodied the “Midwestern values of faith, family and freedom.”

“Hard work, using God-given talents, and loving each other well,” a voice declared over video clips of Ms. Miller, a 63-year-old Illinois Republican, embracing her family, praying and walking on her farm in an ad in early 2020.

“In the world today,” the ad continued, “we could use a lot more of this.”

But there is another side to Ms. Miller’s wholesome image. Since entering Congress, she has routinely vilified Democrats and liberals, calling them “evil” communists beholden to China who want to “destroy” America and its culture. And President Biden’s plan, she seethed on Twitter this spring, is to “flood our country with terrorists, fentanyl, child traffickers, and MS-13 gang members.”

Ms. Miller’s inflammatory words underscore the extent to which polarizing rhetoric is now entrenched among Republicans in the House of Representatives, especially among those like Ms. Miller who voted against certifying the Biden victory, according to an examination by The New York Times of partisan language over the past 10 years.

The analysis of tweets, Facebook ads, newsletters and congressional speeches — more than 3.7 million items in all — relied largely on natural language processing, a technique that uses software to extract information from large amounts of text. The Times tallied words that were linked in academic research to divisive political content, as well as those identified by linguists and computer scientists to be used in polarizing ways — “fascist” and “socialist,” for example, “far right” and “far left.”

Republican representatives have ratcheted up such rhetoric since former President Donald J. Trump took office, the analysis found. In the year and a half after the Jan. 6 Capitol riot, Republicans on average used divisive words and phrases more than twice as often as Democrats in tweets, and six times as often in emails to constituents.

At the forefront of this polarization are Republicans who voted to reject the Electoral College results that cemented Mr. Trump’s defeat last year. A recent Times investigation revealed how those lawmakers helped engrave the myth of a stolen election in party orthodoxy. Now, a Times analysis shows that the language of the 139 objecting members is markedly more hostile than that of other Republicans and Democrats. In their telling, those who oppose them not only are wrong about certain policies but also hate their country.

The Times found that in the current Congress, representatives who fought certifying the election used polarizing language on Twitter about 55 percent more often than other Republicans, and nearly triple the rate of Democrats. Objectors referred to their opponents as “socialist” in more than 1,800 tweets, more than twice as often as other Republicans. Democrats called the other side “fascist” about 80 times.

While provocateurs like Representatives Marjorie Taylor Greene of Georgia and Lauren Boebert of Colorado have etched out combative personas, the analysis found that dozens of rank-and-file members, such as Ms. Miller, also joined the drumbeat of polarization. Ms. Miller, who did not respond to repeated requests for comment, is squarely among the dozens of objectors using the most negative language.

The Times examined Democrats as well as Republicans. In the first years of the Trump presidency, Democrats on average spoke in a more outraged way than Republicans on Twitter and in constituent emails. A few Democrats, including Representative Bill Pascrell of New Jersey, were among those lawmakers who most frequently used demonizing speech on Twitter, even into the current congressional term.

But Republicans have otherwise eclipsed Democrats, the analysis revealed. Republicans have more than quadrupled their use of divisive rhetoric since the early 2010s in the Congressional Record, which is dominated by stately and tedious speeches from the House floor.

Among other things, the algorithmic techniques used by The Times compared statements with one another and with examples of known incendiary language. Similar tools are used in spam filters and by companies tracking discussions about their products on social media. (One complexity is that this technique cannot always distinguish between incendiary rhetoric and factual descriptions of antidemocratic behavior.)

Political scientists at New York University reviewed and corroborated The Times’s findings and said the results underscored a broad shift in Republican rhetoric. “We are clearly living in a time in politics where this kind of aversion is increasing, and also where we are seeing the emergence of an extreme faction in the Republican Party,” said Joshua Tucker, a politics professor and co-director at the university’s Center for Social Media and Politics.

Polarization on the Rise

Five days after the Capitol riot, Representative Kevin McCarthy of California, the Republican leader, implored members of his party to tone down their speech.

“We all must acknowledge how our words have contributed to the discord in America,” he said, according to a recording 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.

Mr. McCarthy added, “No more name calling, us versus them.”

But this spirit of reconciliation did not last. In dozens of tweets since then, Mr. McCarthy has referred to Democrats as “radical” leftists, said they prefer China to the United States and accused them of ruining America.

Mr. McCarthy’s rhetoric is in line with that of other Republicans who objected to the election.

“They are using what are called ‘devil terms’ — things that are so unquestionably bad that you can’t have a debate about them,” said Jennifer Mercieca, a professor at Texas A&M University who studies the history of political rhetoric.

Although a demonizing communication style has been in use for years among media personalities and the occasional firebrand lawmaker, Mr. Trump popularized it among elite politicians. “His party has adopted these strategies as well, because they work,” said Dr. Mercieca, who reviewed The Times’s findings.

The rise of polarization is not limited to Republicans, though their rhetoric tends to be more combative. One of the legislators who has most often lashed out is Mr. Pascrell of New Jersey, who tweets almost daily about Republicans, particularly what he says are their efforts to “overthrow democracy” and install Mr. Trump as a “dictator.”

Mr. Pascrell, in a statement, said Republican leaders were “attacking the legitimacy of our government” and he felt compelled to respond. “I talk about that threat every day in clear, unmistakable terms because it is essential the American people understand what we are facing.”

Members of “the squad,” the group of progressive Democrats that includes Representative Alexandria Ocasio-Cortez of New York, have used that angry language less frequently than most others, despite often voicing far-left views that rattle many Republicans, the analysis found.

Overall, legislators of all stripes are more likely to use provocative language on social media and in Facebook ads than in House speeches and official emails. The majority of messages sent out by congressional offices have remained anodyne — well wishes on holidays, descriptions of services for constituents and details of town hall meetings.

Even so, several political scientists say that the factionalism is alarming because it makes compromise harder and normalizes such rhetoric throughout the population. Messages are particularly pernicious if they claim that political parties hate the United States, are in league with its enemies or cheat to win elections, the experts said.

“The Leftists, who are authoritarians with a DNA that leans toward tyranny, believe that loading up the nation with unskilled workers from underdeveloped nations will provide Democrats with voters,” Representative Andy Biggs, a Republican objector from Arizona, wrote in an email in March 2021.

“Democrats are so enamored of power that they want to legalize cheating in elections,” he added.

On Twitter, objectors described liberals or Democrats as hating America or Americans more than 40 times during this congressional term. Other Republicans used those phrases twice, while one Democrat, Representative Eric Swalwell of California, did so three times.

“Over time, this negative aspect grows like a cancer,” said Monty G. Marshall, longtime director of the Polity IV Project, which collects data on governments worldwide and rates how democratic and autocratic they are. “It’s like a tumor on the body politic.”

‘Negative Partisanship’

Last February, Representative Mike Rogers of Alabama joined the Republican National Committee chairwoman on Twitter accusing the newly elected Democratic district attorney in Manhattan of having “radical pro-criminal” policies.

On its face, the attack had nothing to do with the House of Representatives or its speaker, Representative Nancy Pelosi of California. But Mr. Rogers made it about her.

“Socialism on the march,” he wrote. “We must fire Pelosi.”

That same week, Republicans tweeted more than 180 times about Ms. Pelosi; 165 of those posts were from objectors like Mr. Rogers. The legislators were addressing subjects as varied as a technology bill, the Beijing Olympics and the investigation of Jan. 6.

Their messages were biting: Representative Barry Moore of Alabama wrote, “It’s simple — Speaker Pelosi wants to put America LAST.” Representative Barry Loudermilk of Georgia tweeted, “Speaker Pelosi has turned the people’s House into a dictatorship, and is apparently using her power to try to destroy her political enemies.” And two members retweeted the official Twitter account of the House G.O.P., saying simply, “Pelosi ♥️ Communist China.”

Ms. Pelosi is a favorite target of Republicans: Objectors in the current term mentioned her on Twitter more than “abortion” and “crime,” two of their other frequently used words. Party leaders typically attract criticism, but Democrats posted about Mr. McCarthy, the Republican leader, about 1,100 times, while objectors tweeted about Ms. Pelosi more than 6,000 times.

Objectors referred to Mr. Biden nearly 50,000 times — in more than 20 percent of their tweets — while other Republicans did so about half as often.

Republicans overall mentioned Democrats twice as often on Twitter as they did their own party. Democrats followed the opposite pattern. During the first two years of Mr. Trump’s presidency, Democrats discussed him frequently, though not as much as Republicans now denounce the Democrats.

Even when Republicans have power, vilifying their opponents has worked well for them, said Alan Abramowitz, a political scientist at Emory University. It is part of a broader trend in American politics toward “negative partisanship,” he said. “On both sides there’s a very intense mistrust or dislike of the other party.”

The Capitol Riot

On the first anniversary of the Jan. 6 attack, Representative Betty McCollum, Democrat of Minnesota, sent an email to her constituents calling the event an “attempted coup” and asserting that “our democracy is in danger.”

Ms. McCollum was among dozens of Democrats who sent such missives that week. In a statement to The Times, said she felt obliged to point out the threat posed by the objectors. “I intend to defend our democracy, and if that is ‘polarizing,’ so be it.”

Republicans, on the other hand, had little to say about the riots. Fewer than 20, mostly objectors, published newsletters mentioning the anniversary. And the objectors mainly used it as an opportunity to assail the House investigation of the violence.

“The mainstream media and Democrats’ decision to hold the actions of the few who engaged in violence that day as representative of all those they oppose or as a legitimate attempt to overthrow the government is dishonest,” wrote Representative Randy Weber, a Texas objector.

Representative Matt Gaetz, a Florida objector and one of Mr. Trump’s most vocal proponents, proudly proclaimed that he had “stood up to this singular narrative of ‘threats to American democracy,’” while “most Republicans shied away.” His messages to constituents focused on baseless accusations that F.B.I. informants had incited protesters to storm the Capitol. “We will get the truth out,” he promised.

Hot-Button Issues

It is common fare for House Republicans to vent their frustrations of the moment: government spending, immigration and inflation, for example. But among objectors, those subjects often become slogans of outrage and disdain: the Democrats’ “socialist spending spree,” the “Biden border crisis” and “bidenflation.”

There are telling differences between objectors and other Republicans in both their phrasing and the topics they emphasize, the analysis of their emails to constituents showed.

Those who challenged the election tend to sensationalize hot-button issues, but other Republicans are likelier to focus on mundane subjects: holidays, local meetings and committee work.

In more than 200 emails, objectors tried to stir up fear around efforts to “defund the police” or law enforcement, while other Republicans raised the topic at roughly 60 percent of that rate. Although some progressives have advocated defunding police departments, Democrats used that phrasing only once in their constituent emails, when one wrote, “Don’t defund law enforcement.”

Republicans have turned again and again to problems associated with synthetic opioids like fentanyl, a drug that has ravaged many of the communities they represent and that has barely registered in Democratic communications, according to the analysis. But objectors are more likely to speak about fentanyl in accusatory, hyperbolic tones, blaming Democrats and “open borders” for its rise and seeking to have it labeled a “weapon of mass destruction.”

Objectors particularly stand out in culture-war issues like transgender rights and teaching the history of race in America, weighing in far more often than other Republicans and doing so in a more vitriolic way. In June, Ms. Greene of Georgia raged on Twitter that liberals were “grooming our children, pushing drag queen shows in elementary & middle schools, teaching gender lies and advocating teenagers go through genital mutilation.”

A Media Bubble

The articles and videos that lawmakers share on social media serve as a guide to their most trusted information sources, as well as evidence of a widening gap in the news partisans consume.

Again, the objectors stand out, turning to one source above all others: Fox News. In the most recent Congress, they tweeted links to the network more than 5,300 times, at nearly twice the rate of other Republicans.

Democrats almost never link to Fox, preferring CNN, The Times and The Washington Post. They also link much more frequently to government websites such as those for finding vaccines or health coverage — sites Republicans have almost never promoted.

Objectors differ not only from Democrats but from their fellow partisans in their willingness to direct followers to more stridently right-wing sources, including The Daily Caller, co-founded by the Fox News host Tucker Carlson, and Breitbart News, once led by the erstwhile Trump strategist Stephen K. Bannon. They linked to Breitbart in nearly 900 tweets, compared with about 70 for other Republicans.

“#BidenBorderCrisis costs more lives,” wrote Representative Mo Brooks of Alabama, sharing a Breitbart article about the murder of a woman in Pennsylvania. “When will Socialists support border security?”

The most vocal Trump supporters are also much likelier to link to sites with a reputation for circulating conspiracy theories, including Gateway Pundit and The Epoch Times.

In January, Representative Paul Gosar of Arizona tweeted a link to a Gateway Pundit article about a nonprofit that assists states with voter rolls and registrations. The article accused the group of running “essentially a left wing voter registration drive,” and Mr. Gosar agreed, saying it was an example of efforts by George Soros — the billionaire Democratic donor who is a common target of right-wing conspiracy theories — “to undermine fair elections.”

A spokesman for Mr. Gosar would not address the tweet, instead decrying Democrats’ rhetoric and suggesting that Mr. Biden’s denunciation of extremism and MAGA Republicans counted as “hate speech” against conservatives.

In interviews with The Times, several objectors said that partisan-fueled information wars were a major contributor to polarization and that it was increasingly difficult to know whom to trust — even for them. But some gave surprising answers about their own habits, stating they consumed a greater variety of media than they shared.

“You’ve got to be willing to listen and look at things objectively from people whom you might not be on their radar, or them on yours,” said Representative Pete Sessions of Texas, who said he regularly listened to NPR and The Daily podcast of The Times.

Still, the political news sources he shared on Twitter were Republican staples, with Fox News topping the list.

The Language of Faith

For objectors, evangelical Christianity often shapes their messaging and sometimes their portrayal of the political system as a battleground between right and wrong. They refer to their religion more than other lawmakers, including Republicans, The Times found. And while they often invoke their faith to inspire or celebrate, they also use it to attack Democrats, depicting them as hating Christianity.

“The liberal woke mob are attacking everything. Our National Anthem. Our Christian Faith. Our Gun Rights,” Representative Buddy Carter of Georgia said last year in a tweet. “These people are SICK.”

On social media, Ms. Miller of Illinois regularly quotes the Bible and writes “Happy Sunday” messages to her followers. She posted one such tweet while taking respite from the campaign trail in June, sharing a photo of herself on the sofa with seven of her grandchildren. She wrote, “I am so blessed!”

Five days later, Ms. Miller’s Twitter took a different tone. “The Left tells our children a hopeless message that they do not come from God, they are not born for any purpose, and they cannot obtain salvation,” she wrote, before pledging to defend the right to bear arms.

Last December, Ms. Miller tweeted a picture of a cloven-hoofed sculpture that the Satanic Temple, a self-described nontheistic religious group, had installed near a Christmas tree and Nativity scene inside the Illinois State Capitol. A sign said the state, which is led by Democrats, could not “legally censor” such controversial installations under the First Amendment.

Ms. Miller turned it into a line of attack — tweeting that “the left cheers this” because they “are not only an anti-American party, they are an anti-Christian party.”

“We’re at war for the heart & soul of our country,” she added, concluding, “Christ is on our side and we will prevail!”

Michael H. Keller contributed reporting. Produced by Hang Do Thi Duc and Rumsey Taylor.

Methodology: The Times studied lawmakers’ rhetoric by evaluating nearly three million tweets, more than 100,000 email newsletters, 300,000 Facebook ads and 350,000 statements from the Congressional Record from 2010 through this past June.

The analysis employed language software, Receptiviti, to tally how often the legislators used words that academic researchers had linked to antagonistic speech online.

Times reporters checked thousands of randomly selected tweets and newsletters to see whether the words were indeed being used in a hostile way. This resulted in some words being removed from the evaluation list. Reporters also performed a computer analysis on another large sample to determine which words were much more likely to appear in messages that expressed anger, disdain or distrust toward the opposing party. When negative terms were strongly identified with one party — such as “left-wing” — reporters included a corresponding term from the other whenever possible.

The material went through further analysis. Tweets were counted as polarizing if they included any words from the revised list, but in longer texts such as newsletters, multiple words were required.

The Times worked with Patrick Wu, a postdoctoral fellow at the Center for Social Media and Politics at N.Y.U. Using a technique called trained machine learning, he found the same pattern as The Times in recent tweets.

Ashique KhudaBukhsh, a professor at the Rochester Institute of Technology who researches political polarization, also reviewed the methodology and findings.

To learn about different subjects lawmakers discussed, The Times relied on topic modeling, a machine learning technique that calculates which words are likely to cluster together to form topics. And The Times evaluated religious content using the Linguistic Inquiry and Word Count, a tool that checks texts for related words.

All of these methods are widely used by academic researchers and can evaluate enormous amounts of text, but they are not precise enough to rank individual lawmakers. This is because any given message can produce a false positive or negative. Someone may use an angry word in criticizing such language, for example, or speak in terms too subtle to register as polarizing.

Over hundreds of thousands of examples, these types of errors tend to even out to produce reliable indications of patterns. The Times’s findings about the current congressional term were statistically significant.

The Times obtained data from Twitter; the Congressional Record; Facebook’s Ad Library; the Congressional tracking company LegiStorm; and DCinbox, an academic project that collects email newsletters. Tweets and ads from government accounts as well as campaign accounts were included. The Times collected the data in conjunction with the Tow Center at the Columbia Journalism School.