A growing feud pits Representative Liz Cheney, who has been vocal in her criticism of former President Donald J. Trump, against her colleagues in the House.,

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Tensions among House G.O.P. leaders rise as a possible Cheney ouster looms.

Representative Liz Cheney of Wyoming at the Capitol last week.Credit…Pool photo by Melina Mara

May 4, 2021, 10:07 a.m. ET

Representative Kevin McCarthy of California, the minority leader, said on Tuesday that House Republican lawmakers had expressed concerns to him over whether Representative Liz Cheney of Wyoming, the party’s No. 3, could continue in her position, feeding rising speculation that Ms. Cheney could be stripped of her leadership post.

“I have heard from members concerned about her ability to carry out the job as conference chair, to carry out the message,” Mr. McCarthy said on Fox. “We all need to be working as one, if we’re able to win the majority.”

Minutes after Mr. McCarthy’s interview, a spokesman for Ms. Cheney shot back, suggesting that Ms. Cheney was being unfairly punished for refusing to lie about who won the election.

“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,” the spokesman, Jeremy Adler, said in a statement. “Liz will not do that. That is the issue.”

The back-and-forth highlighted the growing feud between the two leaders, who have taken vastly different approaches to handling the aftermath of the Jan. 6 riot. Ms. Cheney has also been vocal in criticizing President Donald J. Trump and repudiating his false claims that the 2020 election was stolen, and there now appears to be an inevitable confrontation within Republican ranks over whether Ms. Cheney should keep her post.

Mr. McCarthy chose Mr. Trump’s favorite news program, “Fox and Friends,” as the venue for his latest airing of the party’s concerns about Ms. Cheney, whose fate has become a bellwether for the future of the party.

Axios reported later on Tuesday afternoon that Mr. McCarthy went further, citing an unreleased tape of him speaking in the “Fox and Friends” greenroom.

“I think she’s got real problems,” Axios reported Mr. McCarthy as saying of Ms. Cheney off-air ahead of the interview. “I’ve had it with her. You know, I’ve lost confidence.”

When a group of pro-Trump Republicans in the House moved in February to remove Ms. Cheney from her leadership role, citing her decision to vote to impeach Mr. Trump, Mr. McCarthy defended her in a speech just ahead of the secret-ballot vote, which she won overwhelmingly. But in the weeks that followed, Mr. McCarthy soured on her as Ms. Cheney has continued to contradict him, chiefly on whether Mr. Trump should continue to play a leading role in the party.

The turning point came last week at a conference retreat in Orlando, where Ms. Cheney told reporters that any lawmaker who led the bid to invalidate President Biden’s electoral victory in Congress should be disqualified from running for president. She also broke with leading Republicans on the scope of a proposed independent commission to investigate the Jan. 6 riot, saying it should be narrowly focused on the assault on the Capitol, not on Antifa and Black Lives Matter protests, as Mr. McCarthy and others in the party have insisted.

Some lawmakers are so certain that the conference will call a vote to strip Ms. Cheney of her position that they have begun floating names of Republicans who could replace her in the third-ranking post. That endeavor is also fraught. Mindful of the optics of replacing the only woman in leadership with another man, Republicans are eyeing choosing a woman.

Several of them are bullish on the prospect of Representative Elise Stefanik of New York, an outspoken rising star within the party who has toiled to increase the number of women in the party, but it is not clear she would be interested in the job. Also cited as a possibility was Representative Jackie Walorski of Indiana, who as the top Republican on the Ethics Committee earlier this year successfully balanced the job of condemning Representative Marjorie Taylor Greene’s past conspiratorial statements while arguing she should not be kicked off her committees.