The three Republicans vying to replace the departing John Boehner as Speaker of the House took turns meeting behind closed doors Tuesday with a coalition of four groups comprising the chamber's most conservative members.

Lawmakers who attended the forum said House Majority Leader Kevin McCarthy, R-Calif., the current favorite to become speaker, pledged changes to the House.

"I think McCarthy's pitch was `I'm not John Boehner, I'm going to run things differently, I'm my own man,"' said Rep. Blake Farenthold, R-Texas. "And I think that's a case that he does have to make. One of the things I hear all the time from my constituents back in Texas is we don't want John Boehner 2.0."

Lawmakers also said McCarthy addressed his remarks last week about the House Select Committee on Benghazi. In an interview with Fox News' Sean Hannity, McCarthy implied the committee could take credit for Democratic front-runner Hillary Clinton's declining poll numbers. Democrats have charged the remarks prove the committee was set up to harm Clinton politically.

"He did mention he made a gaffe," Farenthold said.

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Rep. Thomas Massie, R-Ky., said McCarthy apologized in the meeting for his comments: "He said it wasn't a good choice of words."

The other two lawmakers running for the job, Reps. Jason Chaffetz of Utah and Daniel Webster of Florida, also addressed the group. Chaffetz told Fox News he would support whoever emerged as the Republican nominee in Thursday's secret ballot.

"At some point we have to unite," Chaffetz said. "Because the last thing we want to do is cede more room to [House Minority Leader] Nancy Pelosi."

Chaffetz chairs the high-profile House Oversight and Government Reform Committee while Webster, who has unsuccessfully challenged Boehner in the past, already has a handful of endorsements from conservatives.

Chaffetz was upbeat as he and his wife left the meeting at the Capitol Hill Club, claiming he'd picked up some support. "I would just fundamentally change the way we do business around here, so it was fun," he said.

The full House votes for a new speaker in open session on Oct. 29. That's when conservatives will have their leverage, because McCarthy can lose only 29 votes to come out the winner. Rep. Mark Meadows, R-N.C. told Fox News that he estimated that approximately 40 House Republicans who were uncommitted about whom they would support.

McCarthy remains the favorite and has Boehner's support, but conservatives say they will not back him unless they're convinced he'll take the House in a new direction. They want more involvement in decision-making and a tough line on issues like raising the federal debt ceiling and deleting funding for Planned Parenthood in must-pass spending legislation -- even though that risks a government shutdown.

"What Kevin has against him is he's John Boehner's right-hand man," said Rep. Tim Huelskamp, R-Kansas, the chairman of the Tea Party Caucus who was elected in 2010.

"He's going to have to reach out and work with conservatives like they've never done since I've been here..

Fox News' Chad Pergram and the Associated Press contributed to this report.