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Retiring House Speaker John Boehner said Monday that the vote for the next speaker would be held Oct. 29 and balloting for all other positions would be delayed until after that in light of the fact Majority Leader Kevin McCarthy, R-Calif., is among the top candidates to succeed him.

In other words, no decision on who might replace McCarthy will be made until after it’s known if he's successful in his campaign to become the next speaker, especially in light of what appears to be a strong challenge from firebrand Utah Rep. Jason Chaffetz, who officially announced his bid on “Fox News Sunday.”

Chaffetz made his bid after McCarthy’s comments last week about the special Benghazi Committee that Democrats say proved the panel was a political front created to pummel the presidential campaign of Hillary Clinton.

Over the past two days, Chaffetz has heightened his rhetoric about why he wants the House’s top post and about being a better candidate than McCarthy.

“There will be a realization that we had better put up a fresh face,” Chaffetz told Fox News on Monday.

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    To win, McCarthy, Chaffetz and Florida GOP Rep. Dan Webster, the third party challenger, will need 218 of the 246 Republican House votes.

    However, the roughly two dozen of the House’s most conservative members who were largely behind Boehner’s Sept. 25 resignation, are not expected to fully support a member of Boehner’s leadership team, like McCarthy.

    Chaffetz, chairman of the House Committee on Oversight and Government Reform, on Sunday said McCarthy had a “math problem.”

    On Monday, he said McCarthy's vote count is “dwindling … not growing.”

    Chaffetz also suggested he was a better communicator than McCarthy.

    “I'm very Margaret Thatcher that way,” he said. “We need to win the vote in the public first. … I didn't wake up and say, ‘Yeah, this was going to be cool.’ ”

    Boehner said he made his decisions after consulting with colleagues and that the new speaker will establish the date for these additional leadership elections.

    “This new process will ensure House Republicans have a strong, unified team to lead our conference and focus on the American people’s priorities,” he said.

    Fox News’ Chad Pergram and Mike Emmanuel contributed to this report.