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The daughter of former Vice President Dick Cheney, who faced criticism from within her party for weeks for not furthering the Republican agenda by calling out Trump, tweeted a clip of the \"Today\" interview Thursday, but notably framed her agenda as an anti-Biden one.

\"Our vision for the future has to be based on policy and substance, and to do that we must embrace the truth,\" the caption said.

The Wyoming representative, who said she is \"absolutely\" running for reelection to the House in 2022, also said Minority Leader Kevin McCarthy \"is not leading with principle right now,\" calling his example \"sad\" and \"dangerous.\"

\"Leader McCarthy's visit to the former president, Mar-a-Lago, was really stunning given what the former president did,\" Cheney continued. \"He provoked an attack on the Capitol -- an attack on our democracy -- and so I can't understand why you would want to go rehabilitate him.\"

While Stefanik, who has pushed Trump's \"big lie\" and challenged results to the 2020 election, remains the front-runner candidate to replace Cheney as the new conference chair, some conservatives critical of her record were pushing to delay the vote and find an alternative nominee with a less moderate history. Stefanik met with members of the conservative Freedom Caucus Thursday in an attempt to address those concerns.

\"Rep.
Evelyn Hockstein/Reuters
Rep. Elise Stefanik, R-N.Y., leaves a House Republican Caucus candidates forum for GOP conference chair, the third ranking leadership position, on May 13, 2021.
>

Any House Republican is allowed to enter the race, but already carrying Trump's support and the endorsement of GOP leadership, Stefanik has told Capitol Hill reporters she's confident she has the votes needed to be elected conference chair, even if anyone else jumped in the race.

While McCarthy, who endorsed Stefanik on Sunday, has branded the removal of Cheney from her leadership post as an issue of unity, the party stripping her of the position may prove more ineffective in perpetuating that message -- as Cheney can now use her microphone to criticize Trump without the confines of a leadership position. She's expected to sit down for more interviews in the coming weeks.

\"PHOTO:
Mandel Ngan/AFP via Getty Images
PHOTO: Rep. Liz Cheney speaks to the media at the US Capitol in Washington, on May 12, 2021.
>

Cheney's ousting and Stefanik's ascension come as it's more mainstream in the Republican Party -- though no less false -- to take up the view that the election was \"rigged\" and recast the Capitol attack as having nothing to do with the former president.

At a House Oversight and Reform Committee hearing Thursday on Capitol Hill, the site of the insurrection, several congressional Republicans downplayed the threat of the Jan. 6 rioters in an attempt to rewrite history. Georgia Rep. Andrew Clyde likened the event to \"a normal tourist event\" and Arizona Rep. Paul Gosar, who has constantly promoted false claims the election was stolen, accused the Justice Department of \"harassing peaceful patriots around the country.\"

Cheney, on \"Today,\" expressed support for a commission to look into the events leading up to Jan. 6 and suggested those in the GOP who don't support one may be hiding something.

\"That kind of intense, narrow focus threatens people in my party who may have been playing a role they should not have been playing,\" she said.

While Wednesday's hearing was underway, shortly after Cheney was ousted from leadership, McCarthy told White House reporters, \"I don't think anybody is questioning the legitimacy of the presidential election. That's all over with.\"

\"PHOTO:
Evan Vucci/AP
PHOTO: House Minority Leader Kevin McCarthy speaks to reporters outside the White House after a meeting with President Joe Biden, May 12, 2021.
>

Asked by ABC News later if Trump is on that same page, given the statements he's released since leaving office challenging election fraud, McCarthy deflected, saying, \"That's President Trump.\"

\"Inside this conference, to do the conference chair job is about the messaging going forward. This has nothing to do about how somebody voted,\" he continued. \"This is simply who's best at delivering the message.\"

Stefanik, likely to deliver that message, was among the 147 Republicans who voted to overturn election results and defended questioning results in a floor speech after the Capitol attack. She has expressed full support for the controversial Republican-backed audit of election results in Arizona, which election experts have worried will further undermine confidence in the electoral process.

Notably, in Stefanik's public pitch to her colleagues for the position released Thursday, she made no mention of the former president or the 2020 election.

ABC News' John Parkinson contributed to this report.

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