As House Republican Conference Chair Liz Cheney, R-Wyo., trades insults with former President Donald Trump over his false claims about the 2020 election, battle lines are being drawn over her future in the party.

On Wednesday, a major Republican voice in the caucus called for Cheney's ouster from leadership: Former President Donald Trump.

Cheney responded in an op-ed in the Washington Post, where she urged the Republican party to "steer away from the dangerous and anti-democratic Trump cult of personality

Less than an hour after Facebook's oversight board upheld his suspension from the social media platform, the 45th president blasted Cheney as a "warmonger" in a statement, claiming she "has virtually no support left in the Great State of Wyoming" while espousing multiple fraudulent statements about the 2020 presidential election. There is no evidence of widespread voter fraud in the 2020 presidential election, a statement backed up by Trump's own attorney general and other federal officials.

Later Wednesday, Trump issued a statement backing New York Republican Rep. Elise Stefanik to replace Cheney as GOP Conference chair: "We want leaders who believe in the Make America Great Again movement, and prioritize the values of America First. Elise Stefanik is a far superior choice, and she has my COMPLETE and TOTAL Endorsement for GOP Conference Chair."

Stefanik thanked Trump in a Twitter post later Wednesday: "Thank you President Trump for your 100% support for House GOP Conference Chair. We are unified and focused on FIRING PELOSI & WINNING in 2022!"

Trump's statement follows that of House Minority Whip Steve Scalise, who became the first Republican leader to publicly call for Cheney's removal and back a challenger to her leadership position.

Scalise released a statement through a spokesperson Wednesday morning backing Stefanik for Cheney's position.

"House Republicans need to be solely focused on taking back the House in 2022 and fighting against Speaker Pelosi and President Biden’s radical socialist agenda, and Elise Stefanik is strongly committed to doing that, which is why Whip Scalise has pledged to support her for Conference Chair," Scalise spokesperson Lauren Fine said in a statement.

In Cheney's op-ed for the Post, she acknowledged that while accepting Trump's election falsehoods in exchange for his support "might seem attractive to some for fundraising and political purposes," the approach could cause long-term damage to the Republican Party and the country.

"I am a conservative Republican, and the most conservative of conservative values is reverence for the rule of law," she wrote. "Each of us swears an oath before God to uphold our Constitution. The electoral college has spoken. More than 60 state and federal courts, including multiple Trump-appointed judges, have rejected the former president’s arguments, and refused to overturn election results. That is the rule of law; that is our constitutional system for resolving claims of election fraud."

"The question before us now is whether we will join Trump’s crusade to delegitimize and undo the legal outcome of the 2020 election, with all the consequences that might have," she continued. "I have worked overseas in nations where changes in leadership come only with violence, where democracy takes hold only until the next violent upheaval. America is exceptional because our constitutional system guards against that. At the heart of our republic is a commitment to the peaceful transfer of power among political rivals in accordance with law."

"History is watching. Our children are watching," she concluded. "We must be brave enough to defend the basic principles that underpin and protect our freedom and our democratic process. I am committed to doing that, no matter what the short-term political consequences might be."

House Minority Leader Kevin McCarthy, R-Calif., put pressure on the No. 3 House Republican in an interview with Fox News on Tuesday, saying that he has “heard from members concerned about her ability to carry out her job as conference chair, to carry out the message.”

“We all need to be working as one if we’re able to win the majority,” McCarthy continued. “Remember, majorities are not given. They are earned.”

Cheney’s spokesperson replied in a written statement: “This is about whether the Republican Party is going to perpetuate lies about the 2020 election and attempt to whitewash what happened on Jan 6. Liz will not do that. That is the issue.” 

McCarthy’s comments come one day after Cheney engaged in a back-and-forth with the former president about his latest false claim about the 2020 election.

Through his post-presidency office, Trump released a one-sentence statement Monday saying: “The Fraudulent Presidential Election of 2020 will be, from this day forth, known as THE BIG LIE!” 

“The Big Lie” is the term popular among critics of Trump and his allies who have repeated false claims that widespread election fraud cost him reelection. 

Cheney, one of the 10 House Republicans who voted to impeach Trump following the Jan. 6 riot at the U.S. Capitol by a pro-Trump mob, fired back on Twitter: “The 2020 presidential election was not stolen. Anyone who claims it was is spreading THE BIG LIE, turning their back on the rule of law, and poisoning our democratic system.” 

Trump later issued a second statement claiming people in Cheney’s state of Wyoming “never liked her much” and noted that he hopes to see Cheney defeated in the state’s GOP primary.

“The President of the United States summoned this mob, assembled the mob, and lit the flame of this attack,” Cheney said in a statement before casting her vote. “Everything that followed was his doing. There has never been a greater betrayal by a President of the United States of his office and his oath to the Constitution. I will vote to impeach the President.”

She also has said she doesn’t believe Trump should have a role in the future of the party and that anyone who supported efforts to block the certification of Joe Biden’s election win should be disqualified as a Republican candidate in the next election. One hundred forty-seven congressional Republicans voted against certifying the results in the hours after the attack on the Capitol.

Further demonstrating the schism between the two GOP leaders, one top Republican congressional aide told The Associated Press that McCarthy had weeks ago urged Cheney to stop talking about Trump, and her failure to do that has boosted frustration with her. 

McCarthy, who delivered a speech supporting her when House Republicans privately voted to keep her in her leadership position in February, will not do that this time, said the aide, who spoke on condition of anonymity to describe internal conversations.

Republicans hoping to oust Cheney from her leadership role lost overwhelmingly during a secret ballot in February, with members of the House GOP voting to keep her in her position with a 145-61 vote.

Underscoring the Republican rift, Cheney criticized Trump anew at a donor event she attended over the weekend with the conservative American Enterprise Institute at Sea Island, Georgia, according to a person familiar with the situation and granted anonymity to discuss it.

“We can’t embrace the notion the election is stolen. It’s a poison in the bloodstream of our democracy,” Cheney said, in comments first reported by CNN. “We can’t whitewash what happened on Jan. 6 or perpetuate Trump’s big lie. It is a threat to democracy. What he did on Jan. 6 is a line that cannot be crossed.”

In another illustration of internal GOP tensions, Cheney and McCarthy have not appeared together at House Republican leadership news conferences for weeks.

On Friday, Rep. Steve Scalise of Louisiana, the second-ranking Republican in the House, told Axios that Cheney is out of step with the party.

"This idea that you just disregard President Trump is not where we are, and, frankly, he has a lot to offer still,” Scalise said.

Rep. Anthony Gonzalez, R-Ohio, however, defended Cheney. 

“If a prerequisite for leading our conference is continuing to lie to our voters, then Liz is not the best fit,” Gonzalez told The Hill. "Liz isn't going to lie to people. Liz is going to say what she believes. She’s going to stand on principle."

Sen. Mitt Romney, another member of the Republican Party who recently faced consternation for his vote to impeach Trump, issued a statement Tuesday afternoon in support of Cheney.

“Every person of conscience draws a line beyond which they will not go: Liz Cheney refuses to lie,” Romney wrote on Twitter. “As one of my Republican Senate colleagues said to me following my impeachment vote: ‘I wouldn’t want to be a member of a group that punished someone for following their conscience.’”

Romney was booed at a Utah state GOP convention over the weekend, but a vote by party members to censure him over his impeachment vote failed.

GOP Rep. Adam Kinzinger of Illinois also showed his support for Cheney, responding to Tuesday's statement from Cheney's communications director about her refusal to whitewash the events of the Jan. 6 Capitol riot, writing, "100 percent. This IS THE ISSUE" in a Twitter post.

Democrats seized on the moment, with House Speaker Nancy Pelosi’s office releasing a mock “help wanted” ad seeking a “non-threatening female.” 

“Word is out that House GOP Leaders are looking to push Rep. Liz Cheney from her post as House Republican Conference Chair – their most senior woman in GOP leadership – for a litany of very Republican reasons: she won’t lie, she isn’t humble enough, she’s like a girlfriend rooting for the wrong team, and more,” the blog post read, referencing reports from CNN and the New York Times.

White House press secretary Jen Psaki referenced the Republican Party schism in Tuesday’s press briefing.

“The Republican Party seems to be spending a lot of blood, sweat and tears trying to figure out where they stand and what they stand for,” Psaki said. “And that's their prerogative.”

“But our focus is on, and how we're spending our time, is defeating the pandemic, growing our economy, building on that for the long run,” Psaki added. “And it’s no secret that the president doesn’t see eye-to-eye on many policies with Congresswoman Cheney, but his view is that the American people elected him, and also many people representing them in Congress, to solve problems for them, and he’s going to continue seeking civility when he disagrees.”

A vote on whether to remove Cheney from her leadership role could occur as early as next Wednesday, when House Republicans are next scheduled to meet. The House is not in session this week.

The Associated Press contributed to this report.