A spokeswoman for House Minority Whip Steve Scalise, the second-ranking Republican in the House, said in a statement on Wednesday that he supported Representative Elise Stefanik, a 36-year-old New York Republican, for replacing Cheney as House Republican Conference chair, reports Xinhua news agency. 

"House Republicans need to be solely focused on taking back the House in 2022 and fighting against Speaker Pelosi and President Biden's radical socialist agenda," said Lauren Fine, the spokeswoman. 

"Elise Stefanik is strongly committed to doing that, which is why Whip Scalise has pledged to support her for conference chair." 

Representative Kevin McCarthy of California, the minority leader and a close ally of Stefanik's, was reportedly pushing Republican lawmakers to privately support Stefanik. 

Stefanik, who not only defended the former President during his first impeachment proceedings in 2019, but also supported a legal action to overturn the 2020 election results, also reportedly got the endorsement from Trump, who gave the New York Republican a shout-out during a speech celebrating his acquittal in the Senate trial of his second impeachment in February, thanking her vigorous support. 

Cheney's spokesperson Jeremy Adler said in a statement Wednesday that the feud between the Wyoming Republican and other rank-and-file House members "is about much more than a House leadership fight", adding: "Liz will have more to say in the coming days." 

Having survived a bid by Trump loyalists in Congress to oust her in February, Cheney, who voted in January to impeach him for inciting the deadly Capitol riot, has been in the hot seat again after her most recent criticism of the former president and his unsubstantiated claim of widespread voter fraud in the 2020 election. 

"The 2020 presidential election was not stolen," Cheney tweeted on Monday. 

"Anyone who claims it was is spreading the big lie, turning their back on the rule of law, and poisoning our democratic system." 

The Republican power reshuffle in the House will have immense implications for the 2022 midterm elections, in which the party vowed to take back majority from the Democrats. 

"We all need to be working as one if we're able to win the majority. Remember, majorities are not given; they are earned. And that's about the message about going forward," McCarthy said in an appearance on Fox News on April 30. 

A vote within the Republican Party to replace Cheney could happen as soon as next week.