Rep. Liz Cheney (R-WY) attends a Congressional tribute ceremony to the late Capitol Police officer Brian Sicknick who lies in honor in the Rotunda of the Capitol in Washington, DC, February 3, 2021.Erin Schaff | ReutersGOP Rep. Liz Cheney, who appears likely to be stripped of leadership duties by her fellow House Republicans, does not plan to stop blasting former President Donald Trump for repeating the lie that the 2020 election was stolen from him, according to people familiar with the matter.Cheney, a staunch conservative, has been telling key donors and supporters behind the scenes that she is going to continue to hold Trump and the Republican Party accountable for what she has called the “Big Lie,” said these people.Her father, former Vice President Dick Cheney, has been involved in these talks as well, the people said.These people declined to be named in this story in order to speak on a private matter.Her stance is likely going to cost Liz Cheney her spot as GOP conference chair in the House. House Minority Leader Kevin McCarthy, R-Calif., has told members to expect a vote on Wednesday to remove Cheney from the position. Rep. Elise Stefanik, R-N.Y., is in line to take over that post. Trump, who has ripped Cheney as a “warmonger,” has endorsed Stefanik for the role.During a call with her allies and top donors late last month, Cheney said she has no intention of backing down from Trump, according to one of the people with direct knowledge of the matter. She has publicly linked Trump’s false claims about the election to the deadly riot on Jan. 6 on Capitol Hill.Cheney, like every other member of the House, is up for reelection next year. Numerous Republicans have announced primary campaigns against her.Cheney was one of 10 House Republicans who voted to impeach Trump in the weeks following the deadly insurrection. Many of her top donors told CNBC last week that they plan to stick with Cheney despite the move by Republicans to oust her from her leadership post.The April call included a small group of supporters, including former Vice President Cheney, one person said. While Dick Cheney has been involved with his daughter’s campaigns in the past, he now finds himself in the midst of a battle for a party he once led along with former President George W. Bush.Dick Cheney, according to people familiar with this call and other recent private gatherings with him, has indicated he supports his daughter’s stance on Trump and the Capitol riot.The April discussion took place before the House Republican retreat and prior to McCarthy publicly taking aim at Cheney in a Fox News interview and other instances.Liz Cheney, in multiple recent private meetings, has told allies that she will likely discuss Trump’s election claims on the campaign trail. She has also acknowledged it could be a challenge to persuade at least some Republicans in her state that Trump’s claims are, in fact, lies.Former Vice President Dick Cheney looks on as his daughter Rep. Liz Cheney, R-Wyo., takes the oath of office on the House floor on Tuesday, Jan. 3, 2017.Bill Clark | CQ-Roll Call, Inc. | Getty ImagesTrump defeated Democrat Joe Biden in Wyoming by over 43 percentage points in 2020. Cheney was recently censured by the Wyoming Republican Party for her vote to impeach Trump.Representatives for Liz Cheney and Trump did not respond to requests for comment. The Wyoming lawmaker recently wrote an op-ed in The Washington Post calling for the party to move on from Trump.”We Republicans need to stand for genuinely conservative principles, and steer away from the dangerous and anti-democratic Trump cult of personality,” Cheney wrote.Still, the apparent unity between Cheney, her father and their associates against Trump and his brand of politics represents an attempt at maintaining power by a faction that seems to have been losing sway in a party that’s largely guided by the former commander in chief.Dick Cheney has not publicly condemned Trump’s stance on the election. People close to him say there is no sign he’s actively lobbying members of Congress to try to help his daughter keep her leadership spot.Liz Cheney, according to Politico, has not been making calls to other Republican officials that could help preserve her position as House GOP chair.