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Washington • Rep. Jason Chaffetz vanquished any doubts Sunday. He is running for House speaker.

"The American public wants to see a change. They want a fresh start," the Utah Republican said on "Fox News Sunday" with Chris Wallace in announcing his long-shot bid. "You don't just give an automatic promotion to the existing leadership team. That doesn't signal change."

Chaffetz argues that elevating current GOP bosses — specifically Majority Leader Kevin McCarthy, R-Calif. — won't offer the sea change that conservatives desire.

Now in his fourth term, Chaffetz is the underdog in the race for speaker. McCarthy was thought to be a lock for the top job after Speaker John Boehner, R-Ohio, said he would resign his leadership role and his seat at month's end.

But Chaffetz said McCarthy can't muster enough backing on the House floor because some 50 of the 247 GOP members won't vote for him. The 188 Democrats are likely to vote for Minority Leader Nancy Pelosi, D-Calif.

"There's really a math problem" for McCarthy, Chaffetz said.

The House GOP caucus will vote Thursday behind closed doors, and by secret ballot, to pick its choice for speaker, and the nominee needs only a majority of those voting there. But, on the House floor, the eventual winner must capture 218 votes to officially take the job.

Rep. Daniel Webster, R-Fla., is the only other candidate in the speaker's race.

The speaker election, to take place later this month, involves a roll call vote in which members are asked individually on the floor whom they support. Chaffetz said he would support the eventual nominee but that he doesn't believe McCarthy can find enough backers to win.

Chaffetz, chairman of the House Oversight and Government Reform Committee, has pitched himself as better at messaging than McCarthy and more able to unite the GOP caucus, often divided between the right-flank conservatives and party centrists.

The Utah congressman says the Republicans have the majority but they haven't, so far, been able to lead because of the fractured caucus.

"We were entrusted by the American people with the largest majority the Republicans have ever had since Babe Ruth was swinging the baseball bat," Chaffetz said on "Fox News Sunday." "But they didn't send us here to perpetuate the status quo."

Chaffetz noted that he had been supportive of McCarthy until the majority leader commented that the House investigation of the 2011 Benghazi, Libya, terrorist attacks had dinged presidential candidate Hillary Clinton's poll numbers, a remark that hinted the probe was about politics.

Chaffetz had quickly criticized McCarthy over the comment, which the majority leader later tried to clarify.

Fox News commentator Brit Hume noted after Chaffetz's appearance, that if it wasn't the Utah congressman who jumped in the race, it would have been someone else. McCarthy's Benghazi comment was "very damaging" and gave Clinton ammunition against the GOP.

"People on the right don't want" McCarthy, Hume said. "He can't win. We're a long way from having this settled."

On Sunday, Chaffetz sent his GOP colleagues a letter asking for their support, noting that many Republicans "have indicated they cannot or will not vote for a current member of our leadership team to be the speaker."

"I am confident I can bridge this divide," Chaffetz wrote, "and work effectively together with all members of our conference."

Chaffetz argues in the letter that he would communicate a "positive and strong message," stand up for core conservative issues, restore "regular order" — meaning bills would come up through committees and not just appear on the floor — and engage with members to ensure they feel valued.