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CNN  — 

Rep. Elise Stefanik, who’s poised to replace Rep. Liz Cheney as the No. 3 House Republican, has signaled to some of her colleagues that she plans to stay in leadership and as chair of the House GOP Conference only through 2022, wanting to pursue the top GOP job on the House Education and Labor Committee next Congress, according to a source with direct knowledge of the talks.

That assurance could help assuage concerns on the right over her more moderate voting record, though she’s widely viewed as a virtual lock for the No. 3 job when the vote happens as soon as Wednesday.

If Stefanik ultimately abides by her private assurance, which was first reported by Politico, there would be an open position and an all-out scramble for the third-ranking spot, which would be the majority whip position if Republicans regain control of the House in next year’s midterms.

The New York congresswoman has been locking up support for the position this week, moving swiftly to clear the field. But concerns remain among some conservatives in the House and around Washington. Outside groups rate her voting record as much less conservative than Cheney’s. And the House Freedom Caucus, for example, has taken issue with Stefanik’s uneven stance on a wide range of issues the group prioritizes, including immigration and LGBTQ rights. She’s expected to address lawmakers in the caucus on Monday, according to a person familiar with the plan.

But even skeptics of Stefanik’s conservative credentials say she’s preferable to Cheney on the most important factor: her loyalty to former President Donald Trump. While the Wyoming Republican and daughter of former Vice President Dick Cheney was a loyal supporter of Trump’s agenda in Congress during most of his presidency, her support for his second impeachment is the only vote that really matters for her leadership position.

Despite her ability to overwhelmingly survive an attempt in February to remove her as conference chair, Cheney’s impeachment vote and her consistent defense of it have enraged the former President. And her continued arguments that the party should move on from Trump and correct his lies about the 2020 election have weakened her position with members who publicly remain in Trump’s camp.

Stefanik’s outspoken loyalty to Trump and his effort to claim the election was illegitimate, on the other hand, appear to be insulating her from anything beyond perfunctory criticism from the conservative activist wing of the party.

There’s wide expectation that Stefanik will win a secret ballot election next week, given that she has the support of Trump, House leadership and a wide cross-section of the conference. And so far, no challenger has emerged to take her on.

Even moderate Republican Rep. John Katko, who voted to impeach Trump and was an ally of Cheney, told a local newspaper he will back his fellow New Yorker for the job, a clear signal that Cheney’s leadership tenure is coming to an end.

“I have every confidence that Elise will be a superb leader for all of our conference, not just some,” Katko told The Auburn Citizen Friday. “Elise and I came in together and she knows me as well as she knows conservatives. She knows that I have a different type of district than a lot of conservatives.”

This story has been updated with additional information.

Michael Warren, Ryan Nobles, Jamie Gangel and Gabby Orr contributed to this report.