Washington — Far-right Republican Rep. Matt Gaetz of Florida said Sunday he will move to oust Speaker Kevin McCarthy from his leadership position after the top Republican relied on Democrats to avert a government shutdown. 

But McCarthy appeared confident that he will keep his job in an interview with "Face the Nation" on Sunday. 

"I'll survive," he said, calling the challenge from Gaetz "personal." "He's more interested in securing TV interviews." 

"Let's get over with it. Let's start governing. If he's upset because he tried to push us into a shutdown and I made sure government didn't shut down, then let's have that talk," McCarthy said. 

McCarthy, a California Republican, turned to Democrats on Saturday to help pass a short-term funding bill to keep the government open until Nov. 17, giving lawmakers more time to pass annual appropriations bills. Conservatives had threatened to oust McCarthy if he leaned on Democrats in his own chamber to avert a shutdown.

"I do intend to file a motion to vacate against Speaker McCarthy this week," Gaetz told CNN's "State of the Union" on Sunday. "I think we need to rip off the Band-Aid. I think we need to move on with new leadership that can be trustworthy." 

McCarthy defended his handling of the short-term measure and dared his detractors to "bring it on."   

McCarthy cut a deal with conservatives in January as he sought to gain enough support to become speaker that allows a single member of the House to force a vote to oust him. The deal helped pave the way for McCarthy to be elected speaker after a grueling four days and 15 rounds of voting. 

But there is no clear successor if McCarthy is removed from the speakership. Republicans have a slim majority in the House and finding a candidate who could satisfy both the right-wing and moderate members of the Republican Party could be an uphill battle. 

Gaetz would need 218 votes to oust McCarthy, meaning he would likely need Democrats to vote with him given Republicans' slim majority. But Gaetz told CNN he has "enough" Republican votes that a week from now McCarthy could be "serving at the pleasure of the Democrats" if he remains speaker. 

Rep. Brian Fitzpatrick, a Republican from Pennsylvania on the House Problem Solvers Caucus, said McCarthy can survive the attempt to remove him from leadership. 

"Are we going to reward bipartisan bills being put on the floor or are we going to punish them? That is a choice," Fitzpatrick told "Face the Nation," saying he would vote to table any such effort. "I don't think that sends the right message. What we need to do is encourage bipartisanship." 

If Gaetz continues to bring a motion to vacate, Fitzpatrick said the rules should be changed. 

"This cannot be the trajectory for the remainder of the Congress," he said. "90%-plus of the American public does not want us to be voting on a motion to vacate every day for the rest of the term." 

In:
• Matt Gaetz
• Kevin McCarthy

Caitlin Yilek

Caitlin Yilek is a politics reporter for CBS News Digital. Reach her at [email protected]. Follow her on Twitter: https://twitter.com/hausofcait

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