Fox hosts and executives privately mocked the former president’s election fraud claims, even as the network amplified them in a frantic effort to appease viewers.“Do we have enough dead people for tonight?”It was a week after the 2020 elections, and Tucker Carlson — along with Fox News executives and other hosts — had watched with panic as Fox viewers, furious and disbelieving at President Donald J. Trump’s defeat, began to turn against the top-rated network. The viewers believed Mr. Trump’s claims that a widespread conspiracy of voter fraud was behind his loss. And as Mr. Carlson’s nightly 8 p.m. hour approached, the host pushed his producers to give the viewers what they wanted.He demanded examples of dead people voting in Nevada or Georgia, even offering to call the Trump campaign personally to ask for help. That night, he trumpeted the evidence, borrowed from a Trump campaign news release: Four allegedly dead Georgians had cast ballots. Within days, though, the campaign’s spoon-fed examples began to fall apart. Three of the dead Georgians were actually alive. And Mr. Carlson was forced to partly retract his allegations, while insisting to viewers that “a whole bunch of dead people did vote.”Mr. Carlson told his viewers on Nov. 11, 2020, that dead people had cast ballots.Mr. Carlson’s frantic effort to appease angry Fox viewers, revealed in texts and emails released as part of a $1.6 billion defamation suit against Fox News by Dominion Voting Systems, underscore the central quandary faced both by Fox and the Republican Party in the wake of Mr. Trump’s defeat and still today, as the former president mounts another campaign for the White House.Like the Republican Party more broadly, Fox wants and needs the support of Trump fans, who both dominate party primaries and form the core of Fox’s viewership. And like the party, Fox has found it difficult to quit Mr. Trump even as his manic efforts to relitigate his defeat have hobbled the party in subsequent elections.Fox News has been the most trusted and watched source of information for conservative America for decades, and its frequent symbiosis with the Republican Party is well established. But the internal documents released in recent days have provided an unprecedented glimpse into network decision-making as its dual imperatives — to keep its base audience of conservatives satisfied and meet its promise to maintain journalistic standards of fairness and factuality — came into conflict as never before.No figure is more central to that conflict than Mr. Carlson. Ever since taking over Fox’s 8 p.m. hour in 2017, Mr. Carlson had maintained a carefully calibrated distance from Mr. Trump, using inflammatory segments about a border invasion and the “replacement” of native-born Americans by immigrants to appeal to Mr. Trump’s base — while minimizing how often he discussed Mr. Trump, whom he regarded as erratic and undisciplined. “We are very, very close to being able to ignore Trump most nights,” Mr. Carlson texted with staff members in early January 2021, adding, “I hate him passionately.”But in the months after the Jan. 6 attacks, “Tucker Carlson Tonight” doubled down on a pro-Trump narrative that both Mr. Carlson and his bosses knew was rooted in a lie. According to a New York Times analysis, in 2021 nearly half of Mr. Carlson’s shows — more than 100 episodes — featured segments downplaying the Capitol riot, casting the insurrectionists as innocent citizens seeking legitimate redress for election fraud, and suggesting the riot itself was a “false flag” operation orchestrated by federal law enforcement to entrap Trump supporters.His efforts to rewrite the events of Jan. 6 again took center stage this week, just as reams of emails, texts and deposition transcripts from the Dominion suit revealed that the network’s hosts and executives knew they were peddling lies to their own viewers.On his show this week, Mr. Carlson once more recast the violent attack that took place in January 2021 as a largely peaceful protest, this time using previously unreleased surveillance footage provided to his show by the new Republican House speaker, Kevin McCarthy. Mr. McCarthy, whose campaign for the speakership was backed by Mr. Trump, provided the footage after Mr. Carlson suggested on his show that releasing the tapes would help Mr. McCarthy overcome conservative resistance to his bid.On Mr. Carlson’s show on Monday, he described the Jan. 6 riot as a largely peaceful protest.On air, Mr. Carlson accused a Democratic-led congressional committee of misleading the public about what really happened. “Committee members lied about what they saw, and then hid the evidence from the public,” Mr. Carlson charged.News outlets and fact checkers found the broadcast rife with inaccuracies and false claims. Republicans in the House, among whom loyalty to Mr. Trump remains strong, defended Mr. Carlson’s segment. But Republicans in the Senate — currently controlled by Democrats, after Trump-backed candidates went down to defeat in the 2022 elections — attacked the powerful Fox host in unusually blunt terms.“It was a mistake, in my view, for Fox News to depict this in a way that’s completely at variance with what our chief law enforcement official here at the Capitol thinks,” said Senator Mitch McConnell of Kentucky, the minority leader.In the pretrial public relations maneuvering, Fox News has accused Dominion of using its court filings to share selective and out-of-context portions of internal text messages to “smear Fox News,” part of a broader effort to “silence the press” through a winning verdict. In a statement, a network spokeswoman said, “Fox News will continue to fiercely protect the free press as a ruling in favor of Dominion would have grave consequences for journalism across this country.” In defending Mr. Carlson’s coverage of Mr. Trump’s voter fraud claims, Fox executives have also pointed to Mr. Carlson’s on-air criticism of a lawyer behind some of the most outrageous voter fraud charges, Sidney Powell.Documents released in the Dominion lawsuit illustrate in vivid detail Fox’s complex relationship with the Republican Party, with the network serving variously as custodian, enforcer and powerful interest group in its own right.Senator Mitch McConnell pushed back against Mr. Carlson’s characterization of the Capitol attack.J. Scott Applewhite/Associated PressDuring the election, Dominion has alleged, Fox’s chief, Rupert Murdoch, personally gave Mr. Trump’s son-in-law and adviser, Jared Kushner, a preview of at least one Biden campaign ad. After the election, Mr. Murdoch called Mr. McConnell and asked him to lobby other Republican senators to avoid endorsing Mr. Trump’s claims of widespread voter fraud. At moments, Mr. Murdoch and a top editor at the Murdoch-owned New York Post discussed editorials intended to encourage Mr. Trump to accept his defeat gracefully, seemingly in hopes of avoiding further damage to the party.In mid-November 2020, Mr. Murdoch emailed Fox’s chief executive, Suzanne Scott, explaining the need for Fox to reorient away from Mr. Trump’s conspiracy theories and focus on the Georgia special senate elections, with Fox “helping any way we can.”Top Fox personnel agonized over the difficulty of escaping Mr. Trump’s influence over their own audience. “This day of reckoning was going to come at some point — where the embrace of Trump became an albatross we can’t shake right away if ever,” Dana Perino, a prominent Fox host, wrote to a friend in November 2020.Yet the shoals they were trying to navigate had been in no small part laid by Mr. Carlson, one of Fox’s most-watched hosts. Though the newly released messages show Mr. Carlson expressing skepticism in his private emails about the extent of “voter fraud,” he had been an early and energetic promoter of the doubt Mr. Trump was trying to sow.Within 24 hours of the polls closing, he declared that the election had been “seized from the hands of voters,” and that the final results would finally be determined by “lawyers and courts and clearly corrupt, big-city bureaucrats.” Americans “will never again accept the results of a presidential election,” he predicted.After the major networks declared Mr. Biden president-elect, Mr. Carlson reminded his viewers that troubling questions remained: “We don’t know how many votes were stolen on Tuesday night; we don’t know anything about the software that many say was rigged,” he said. His audience members, he said, were being played for suckers: “They knew you were coming. They laughed at you when you left.”But behind the scenes, Mr. Carlson and his producers were among those scoffing.In the days before the Jan. 6 attack on the Capitol, they discussed their intense hopes that Mr. Trump would soon leave the political scene. They mocked his plans to block the certification of Mr. Biden’s win and raged at how Mr. Trump’s lawyers had undermined their own arguments about fraud with sweeping conspiracy theories and debunked allegations.Two weeks after the election, Mr. Carlson, his executive producer and a top Fox executive named Ron Mitchell traded texts about a news conference at which one of Mr. Trump’s lawyers, Rudolph W. Giuliani, unspooled a litany of debunked allegations while hair dye dripped down his face. “I don’t see how to cover this,” Mr. Mitchell wrote. (That night, Mr. Carlson devoted his opening monologue to the news conference, carefully asserting that Mr. Giuliani “did raise legitimate questions and in some cases, he pointed to what appeared to be real wrongdoing.”)Mr. Carlson has claimed to “never look at the ratings” for his show. But Dominion texts show Mr. Carlson, his bosses and his fellow hosts obsessing over them. Within weeks of the election, it became clear to them that Fox viewers badly wanted them to focus on supposed evidence of voter fraud.“Tucker wrote me and Laura and said last nights numbers were a disaster,” Sean Hannity wrote to Fox producers in late November 2020, referring to Mr. Carlson and Laura Ingraham. (His executive producer, Robert Samuel, noted that the previous week’s most highly rated programming minutes “were on the voting irregularities.”) Mr. Carlson had also texted the two other hosts about ratings earlier that month, joking that an angry Fox viewer who had ranted against the network on Twitter would get “way better numbers than what we have” and warning Mr. Hannity that “the 7:00 was third last night,” referring to the time slot immediately preceding his own.As Mr. Carlson’s broadcast was coming to an end on Nov. 10, a Fox staff member warned the host that he was being attacked on Twitter for not covering allegations of voter fraud. “It’s all our viewers care about right now,” the staff member wrote. Mr. Carlson replied that it had been a “mistake” but that “I just hate” the topic.That night and the next morning, Mr. Carlson and the unnamed colleague brainstormed how to get into the story, trading links and tweets, eventually seizing on a local news report in Nevada suggesting a woman who had died in 2017 had voted there in November. (An investigation later determined that the woman’s husband, a Republican, had used her ballot to vote twice, then claimed her ballot had been stolen.) They debated whether they could “get up to five examples of specific names of dead people that voted,” and reached out to Jason Miller, a Trump campaign official, asking for evidence that they could then present on “Tucker Carlson Tonight.”“Obviously they need to do whatever they can to help us,” Mr. Carlson told his Fox colleague.On the afternoon of Nov. 11, as the next evening’s broadcast approached, the staff member texted Mr. Carlson again.“Have you seen last night’s numbers?” the staff member wrote, adding, “It’s a stupid story but this is all the viewers are into right now.”Mr. Carlson replied: “I noticed.”Julie Tate More