House Minority Leader Kevin McCarthy said Tuesday that Republican lawmakers have shared concerns with him over Rep. Liz Cheney's ability "to carry out the message," fueling speculation that the No. 3 House Republican may once again face an effort to oust her from party leadership.

"There's no concern about how she voted on impeachment — that decision has been made," the California Republican told Fox & Friends. "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."

His comments come a day after Cheney responded to a statement from former President Donald Trump once again perpetuating his false claim the presidential election was stolen from him.

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

The Wyoming lawmaker, the highest-ranking woman in House GOP leadership, has faced intense backlash from her party since she voted to impeach Trump over his role in the Jan. 6 insurrection.

"There has never been a greater betrayal by a President of the United States of his office and his oath to the Constitution," Cheney said in a statement at the time.

Her vote earned her a censure from the Wyoming Republican Party and a growing list of primary challengers, along with calls to throw her out of her leadership job. She was able to ward them off in a secret ballot vote in February with support from McCarthy.

But since then, the gulf between Cheney and the rest of GOP leadership has grown as McCarthy and Minority Whip Steve Scalise are embracing the former president to help Republicans in the next midterm elections.

"This idea that you just disregard President Trump is not where we are, and frankly he has a lot to offer still and has offered a lot. He wants to help us win the House back," Scalise recently told Axios.

Last month, Cheney, who is responsible for party messaging, pointedly did not invite Trump to speak when Republicans gathered for their annual retreat in his home state of Florida. Once there, she told reporters that any Republican who objected to the Electoral College counts should not ever be considered a GOP candidate for president.

"I do think that some of our candidates who led the charge, particularly the senators who led the unconstitutional charge, not to certify the election, you know, in my view that's disqualifying," she told the New York Post.

Cheney has also broken with party leaders who are blocking an investigative commission into the Jan. 6 attack because they want it also to examine the violence around some of the racial justice protests last summer. Democrats said that's a distraction, and Cheney agreed.

"I think that's a different set of issues, a different set of problems and a different set of solutions," she said at the retreat. "And so I think it's very important that the Jan. 6 commission, focused on, what happened on Jan. 6 and then what led to that day."

The strain between Cheney and GOP leadership was on full display at a press conference at the end of February when reporters asked McCarthy whether Trump should speak at the Conservative Political Action Conference.

"He should," McCarthy answered bluntly. The question was then posed to Cheney, who answered from the back as McCarthy remained at the lectern.

"I've been clear in my views about President Trump and the extent to which following Jan. 6 I don't believe that he should be playing a role in the future of the party or the country," Cheney said, as McCarthy closed his eyes in apparent frustration.

An awkward pause followed, with McCarthy abruptly ending the press conference with "on that high note, thank you very much." The pair left walking in separate directions and have rarely appeared together since then.

Professor Jim King of the University of Wyoming said Cheney's opposition to Trump hasn't yet ruined her political fortunes, but it has changed them.

"She may not any longer be on track to be speaker, but I don't see that she's in a position where she's going to lose in Wyoming," he said.

Fundraising for her reelection bid has been robust, and she continues to enjoy support from Republicans such as former House Speaker Paul Ryan as well as fellow Republicans who also supported Trump's impeachment.

"Every person of conscience draws a line beyond which they will not go: Liz Cheney refuses to lie," Sen. Mitt Romney, R-Utah, tweeted Tuesday.

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