(WASHINGTON) — As House Republican leaders actively kept trying Wednesday to oust a member of their own leadership team – No. 3 Rep. Liz Cheney – the congresswoman wasn’t backing down — but she wasn’t openly fighting the move, either.

The embattled Wyoming representative has told people she doesn’t believe it’s worth serving as the Republican Party’s conference chair if it requires lying about the election results, a source familiar with the congresswoman’s thinking told ABC News.

Cheney has angered her Republican colleagues in the days and weeks following the Jan. 6 Capitol riot by repeatedly calling out former President Donald Trump’s election lies, which she said she believes played a major role in inciting the insurrection.

In February, Cheney fought off a challenge to boot her from the coveted leadership position due to similar circumstances, though at the time she still had the support of top Republican leadership.

Cheney kept her leadership role after a closed-door GOP 145-61 vote with a secret ballot that required two-thirds support of the conference to remove her.

It’s not clear whether that threshold or format will change in any upcoming vote. A spokesman for House Republican Leader Kevin McCarthy did not respond to messages about the format of a conference vote.

And it’s unclear if Cheney can hold on to the spot this time around. Sources have told ABC News that a vote to boot Cheney could take place as soon as next Wednesday, during a House Republican conference-wide meeting.

Jeremy Adler, a spokesman for Cheney, signaled Wednesday morning that the congresswoman will not sit back quietly as the intra-party attacks continue.

“Liz will have more to say in the coming days,” he said. “This moment is about much more than a House leadership fight.”

Cheney is not actively whipping colleagues for their support to keep her in the position, a source close to Cheney said.

The congresswoman believes that evading questions about Trump and the election results rather than forcefully answering them — as other GOP leaders have done — is equivalent to “being complicit in the lie,” the source said.

“If you let [Trump] bloviate, you get people attacking the Capitol and you get people attacking the very foundation of the Republic,” the source said in explaining the thinking behind her repeated comments since Jan. 6.

On Wednesday, Trump himself weighed in to criticize Cheney as a “warmongering fool who has no business in Republican Party Leadership.”

Trump has endorsed Rep. Elise Stefanik of New York in the race to replace Cheney.

“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. Elise is a tough and smart communicator!”

Stefanik has emerged as the apparent frontrunner should Cheney be ousted from her post, sources familiar with the matter told ABC News.

Stefanik, a prominent ally and defender of Trump, has been working the phones with her team in a bid for Cheney’s spot, sources said.

In January following the insurrection at the U.S. Capitol, the dean of Harvard’s Kennedy School of Government announced Stefanik was removed from the advisory board of the Harvard University Institute of Politics after her “public assertions about voter fraud in November’s presidential election that have no basis in evidence, and she has made public statements about court actions related to the election that are incorrect.”

McCarthy’s team has begun whipping votes against Cheney and after McCarthy was caught on a hot mic in audio obtained by the Daily Caller saying he’s “had it” with Cheney.

“I think she’s got real problems. I’ve had it with …I’ve had it with her. You know, I’ve lost confidence,” McCarthy said in audio published by the Daily Caller.

Other Republican leaders have publicly weighed in to support Stefanik.

“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,” a spokesman for Republican Whip Steve Scalise said in a statement provided to ABC News.

President Joe Biden offered his first reaction to House Republicans’ effort to oust Cheney, telling reporters Wednesday, “I don’t understand the Republicans.”

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