Updated: 10:19 a.m. | Oversight and Government Reform Committee Chairman Jason Chaffetz will run for speaker.

The Utah Republican announced his decision on Fox News Sunday, citing support from colleagues who “recruited” him to challenge the establishment favorite, Majority Leader Kevin McCarthy, R-Calif.

“We don’t want to fight internally,” Chaffetz told Fox News anchor Chris Wallace, “but realistically we can’t vote to promote the existing leadership.

“Kevin McCarthy’s a good man,” Chaffetz said, “and he’s a reason we have such a solid majority. But things have changed, and there’s really a math problem.”

Chaffetz granted that McCarthy may have the majority of votes to win a secret-ballot fight behind closed doors on Thursday to be the party’s official nominee to replace resigning Speaker John A. Boehner.

But Chaffetz also asserted McCarthy lacks a critical bloc of support from at least 50 conservatives. That’s 50 votes McCarthy has to have if he has any hope of getting the necessary 218 votes in the live roll call vote that comes later on the House floor, when Democrats will participate.

In that scenario, unless Democrats or conservatives relent on the floor, Republicans would have to pick a new replacement for Boehner other than McCarthy. And part of Chaffetz’s calculation appears to be the belief that Republicans could then settle on him — or even that Republicans may look to save themselves the embarrassment of a floor fight for speaker and just coalesce around his candidacy.

“You have a growing number of [Republican conservatives] that will not and cannot vote for Kevin McCarthy as speaker on the House floor,” Chaffetz told host Chris Wallace.

Asked whether he himself was prepared to support the conference’s nominee during the House floor vote, Chaffetz was cagey.

“I will support the nominee,” he said, “but I just don’t believe the nominee, if it’s Kevin McCarthy, can get to 218.”

Rank-and-file Florida Republican Rep. Daniel Webster is also running to succeed Boehner.

In the interview, Chaffetz hinted his speakership style would be conservative, confrontational to President Barack Obama’s administration and inclusive of all members of the House Republican Conference — all things that members who are lukewarm on McCarthy want to hear.

But Chaffetz also indicated he would perhaps not be a willing partner in budget negotiations to raise sequester caps — a condition of being able to pass a long-term government funding bill, given the White House’s promise to veto any legislation that maintains those current spending levels.

“I just don’t believe we can continue to add to the deficit so I, personally, like the budget caps,” he said. “I do believe we need more money for the military, we need more money for the VA — we need to take care of the people who are taking care of us. And I want to fight cancer … but, again, it’s not my personal agenda. As speaker you have to take the will of our body.”

Chaffetz added he didn’t support raising the debt limit without conditions, which could end up being his first major task as speaker if Boehner doesn’t tackle the matter before he leaves at the end of October: The deadline to increase the debt ceiling is Nov. 5.

“Our job in the House is to actually put forward a bill. I would like to see it actually cut the deficit … not just keep punting it down the road,” he said. “We’re not just gonna unilaterally raise the debt limit. I don’t think that’s the responsible thing to do.”

Wallace asked whether an episode earlier this year would be any indication of what members could expect of a Chaffetz speakership — when Chaffetz took a subcommittee chairmanship gavel away from Rep. Mark Meadows, R-N.C., in retaliation for going against leadership in a procedural vote on the House floor. That incident led to backlash from the House Freedom Caucus that culminated in Meadows’ reinstatement.

“I think I learned from that lesson,” Chaffetz explained, “That you’re not gonna do things by cutting people off at the knees. I think I was a good leader in that I listened for an hour and 40 minutes with my committee and reconsidered that decision. We gotta win the argument and make the case, not just knock people over the head if they don’t do what we’re gonna do.”

Chaffetz earlier in the week criticized McCarthy for suggesting on another Fox News program that the Benghazi committee’s major accomplishment so far was helping to sink poll numbers for 2016 Democratic presidential front-runner Hillary Rodham Clinton, even asking the majority leader to apologize. Democrats have been having a field day with the rhetorical flap, and Republicans have begun to question both privately and publicly whether McCarthy is ready for primetime.

On Sunday, Chaffetz said, “We want a speaker who speaks. We need someone who’s out there, who is actually going out there and making the case to the American people, talking to the Senate about what we need to do and going on the national television shows and winning that argument.

“We don’t seem to win the argument,” he said, “and that’s a problem.”