CNN  — 

Cindy McCain, widow of longtime Republican Sen. John McCain of Arizona, on Tuesday warned that Republicans need to exercise caution as the party mulls ousting its No. 3 in House GOP leadership.

Asked by CNN’s Chris Cuomo for her thoughts on Rep. Elise Stefanik, a vocal defender of former President Donald Trump who is emerging as the main contender to potentially replace Rep. Liz Cheney in the party leadership, McCain said in part: “We do need to be careful.”

“It doesn’t serve any good if we just oust someone who really is a good representative of the party,” said McCain, an establishment Republican and staunch Trump critic.

McCain’s comments come as Cheney faces backlash from much of her party over the Wyoming Republican’s ongoing clash with the former President as she’s called out his lies about the 2020 election. House Republican leader Kevin McCarthy has contended that Cheney has failed to do her job in driving the party’s message to take back the majority, with a hot mic on Tuesday catching him saying, “I’ve had it with her.”

Stefanik, a New York Republican, is working behind the scenes to lock down enough support to replace Cheney as the No. 3 in GOP leadership, multiple Republican sources told CNN on Tuesday, moving swiftly to clear the field to ascend to the powerful position.

So far, no challenger to Stefanik has emerged – and at least two potential candidates have indicated they won’t mount bids, increasing the likelihood that she will take the influential position.

Members of the House GOP leadership are quietly backing Stefanik’s ascent to the post, the sources said, a rapid turn of events amid Cheney’s bitter feud with Trump, which has left her increasingly isolated in the House GOP Conference.

McCain on Tuesday also reiterated her willingness to serve in the Biden administration should the opportunity arise.

“I would serve in any capacity if the President were to ask me to do so, yes, I would,” she told Cuomo when asked if she would consider taking a position if offered one by the administration.

CNN’s Annie Grayer, Manu Raju and Lauren Fox contributed to this report.