GOP leader questions whether Cheney can do job after she blasts Trump's 'BIG LIE' comment

House Republican Leader Kevin McCarthy said on Tuesday a growing number of Republicans in the conference are taking issue with Rep. Liz Cheney and he signaled that her days as GOP Conference chair -- the third-ranking Republican in the House -- could be numbered.

"I have heard from members concerned about her ability to carry out the 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 said on Fox News.

While he did not explicitly state what her future will be within the party, all signals point to another possible vote to oust her from her position as conference chair.

"I haven't heard members concerned about her vote on impeachment, it's more concerned about the job ability to do and what's our best step forward that we can all work together instead of attacking one another," he said.

Cheney's team was quick to respond.

"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," Cheney spokesman Jeremy Adler said in a statement provided to ABC News.

The latest battle in Cheney's political war with President Donald Trump over the election came Monday when Trump put out a statement saying, "The Fraudulent Presidential Election of 2020 will be, from this day forth, known as THE BIG LIE!"

"The 2020 presidential election was not stolen," Cheney tweeted not long after. "Anyone who claims it was is spreading THE BIG LIE, turning their back on the rule of law, and poisoning our democratic system."

Cheney rebuked Trump again on Monday at a closed-door conference in Georgia, where a spokesman confirmed she called Trump’s false election fraud claims "a poison in the bloodstream of our democracy."

The earliest Republicans could hold a vote on Cheney's leadership position is next Wednesday during a weekly Republican conference meeting, though sources have signaled a vote could take place before the end of the month.

Republicans are considering another woman to replace Cheney, sources familiar with the deliberations told ABC News. Some of those names under consideration are Reps. Elise Stefanik, Anne Wagner and Jackie Walorski, the sources said. Axios was first to report their names.

A spokesperson for Wagner declined to comment. Spokespeople for Stefanik and Walorski did not immediately respond to requests for comment.

Stefanik has emerged as the apparent front-runner should Cheney be ousted, sources familiar with the matter told ABC News.

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

Following the insurrection at the U.S. Capitol, the Dean of Harvard University's Kennedy School announced Stefanik was removed from the advisory board of Harvard's 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."

GOP Rep. Jim Banks is also being considered, per a source. The Indiana Republican heads the Republican Study Committee. ABC News has reached out to Banks' office for comment.

The optics of replacing Cheney, the only woman in House Republican leadership, with a white male, would certainly raise some eyebrows at a time when the Republican Party is trying to engage more women and minorities in politics.

Frustration is growing among Republican lawmakers at the continued feud and Cheney's seeming inability to step away from the political battlefield.

"GOP members want to focus on the agenda. We have energy issues we want to focus on, and this isn't helping at all," one GOP aide said of the broader intra-party fight.

As a conference chair, Cheney's role is to maintain focus on the party's message, and not necessarily her own, having some in the party admitting she could very well be in jeopardy of losing her leadership post.

"She's there telling the truth, but she needs to think about how effective she is able to be if she's constantly choosing to engage opposite Trump which puts her opposite most of the conference. If she can't develop some message discipline, then what is the point in her retaining the job," another Republican aide told ABC News.

In a secret ballot in February, Republicans voted 145-61 to keep her in the No. 3 position, despite her vote to impeach Trump for his alleged role in inciting the Jan. 6 Capitol insurrection.

McCarthy, who at the time was criticized by colleagues for his shifting statements about Trump’s responsibility for the storming of the U.S. Capitol, endorsed Cheney and encouraged Republicans to keep her on the leadership team.

Now, it appears McCarthy is not as confident in Cheney’s role in leadership as he looks to take back the House in 2022 and win back favor with the former president.

McCarthy, when asked last week about Cheney’s future, refused to answer when asked whether she remained a good fit as the conference chair. Members of McCarthy's team have begun whipping votes against Cheney.

Cheney has taken heat from other Republicans for statements she has made in recent weeks and months to direct the Republican Party away from Trump.

Trump, in return, has vowed to back a primary challenge to Cheney in her statewide district in Wyoming.

In February, Cheney told reporters that Trump "does not have a role as a leader of our party going forward.”

Last week, she said it is "disqualifying" for any public official who opposed certifying the election results to run for the White House in the future.

At the Republican retreat in Orlando last month, Cheney said that she believes Senate Minority Leader Mitch McConnell and McCarthy are the heads of the Republican Party and suggested that the GOP can win back the House, Senate and White House in the next elections by conveying to voters that they are a party of "competence and of conservative principles" and by winning back voters they lost in 2020, making subtle digs against the former president without naming him.

One Republican official with knowledge of the matter told ABC News that Cheney is unlikely to lose McConnell’s support, given there’s no need for him to weigh in on the matter. McConnell also has a longstanding relationship with the Cheneys.

Just last week, conservatives criticized Cheney for fist-bumping President Joe Biden as he walked into the House chamber to deliver his address to a joint session of Congress.