By Sunlen Serfaty, Alex Rogers and Jamie Gangel, CNN

(CNN) -- A private squabble between a small group of prominent House Republicans on Tuesday renewed the debate on the future of the party, as some factions argue that they should never falter in following President Donald Trump and others urge a return to their conservative, hawkish worldview.

After returning to Washington, DC, this week, some of Trump's loudest supporters in Congress attacked Rep. Liz Cheney, the number three Republican in the House, upset that she broke with the President on a number of issues and supported Dr. Anthony Fauci, the nation's leading infectious disease expert, during the coronavirus pandemic.

Ohio Rep. Jim Jordan, who has needled his party's leadership while seeking to supplant them in the past, led part of the discussion, according to sources granted anonymity to describe a private meeting. Cheney is viewed as someone who could one day lead the House Republican conference and Jordan, who has run for the top spot before, still has leadership ambitions, multiple sources told CNN.

A handful of House firebrands criticized the Wyoming congresswoman for supporting the Republican primary opponent of Kentucky Rep. Thomas Massie, who had drawn Trump's ire in the spring for forcing House members to return to the Capitol for a vote on a stimulus bill amid the outbreak. Jordan listed areas where Cheney disagreed with Trump, including her resistance to the President's plan to pull back troops in Germany and Afghanistan. And Texas Rep. Chip Roy of Texas, facing a tough reelection, hit Cheney for supporting Fauci and complained that his Democratic opponent has retweeted some of Cheney's tweets. After the meeting, Rep. Matt Gaetz of Florida called on her to "step down or be removed" from her leadership position.

In an interview with CNN's Brianna Keilar, Roy said that questions regarding the meeting involve "a whole lot of palace intrigue about what's being said in Washington," called Cheney a "friend" and made clear that he is not calling for her to step down. The Texas congressman said he raised in the meeting that the country needs to elevate other trusted public health experts besides Fauci, including those who argue against the strategy of locking down the country.

Cheney noted in an interview with Fox News on Wednesday that she votes with Trump almost all of the time and when she disagrees with him, it is usually in favor of a more hawkish stance on foreign policy matters.

Trump weighed in on Thursday morning, tweeting that Cheney "is only upset because I have been actively getting our great and beautiful Country out of the ridiculous and costly Endless Wars."

"I am also making our so-called allies pay tens of billions of dollars in delinquent military costs," he added. "They must, at least, treat us fairly!!!"

Cheney responded to Trump's tweet Thursday by saying in a statement to CNN, "It's no surprise the President and I have some disagreements on foreign policy. As a member of the House Armed Services Committee, I have no more important duty than providing for the defense of the nation, and I will continue to speak out on these issues."

In the Fox interview, Cheney said she was in a "good place" with Massie, who won his primary, after their "nice, long talk" yesterday. Cheney also turned her sights on the Democrats.

"The conference meeting yesterday opened with, and was focused on, what America will look like if Joe Biden and Chuck Schumer and Nancy Pelosi are running this country, and how important it is for us all to be unified against that," said Cheney.

"Whether or not we have debates and discussions internally, as I'm sure we will continue to do, we are going to be absolutely united going forward on the big issues," she said. "I'm not going anyplace."

This story has been updated with additional developments Thursday.