Rep. Daniel Webster (R-FL) listens to the roll call vote for the Speaker of the House inside the House chamber on January 6, 2015 in Washington, DC. Webster won 12 votes during his unsuccessful challenge of Speaker of the House John Boehner (R-OH). (Photo by Chip Somodevilla/Getty Images)

A group of hard-line conservatives threatened to upend the Republican race to succeed outgoing House Speaker John A. Boehner, announcing on Wednesday it will throw its support behind a little-known Florida lawmaker to become the next speaker.

The House Freedom Caucus’s backing of Rep. Daniel Webster (R-Fla.) ahead of a crucial internal party vote Thursday deeply complicates Majority Leader Kevin O. McCarthy’s bid to succeed Boehner. The group counts enough members — about 40 — to deny McCarthy the majority of the whole House he would need to claim the speaker’s chair.

But in an opening for the California Republican, caucus members said Wednesday that the endorsement is binding on members only for Thursday’s party vote and that it would not necessarily apply to the decisive Oct. 29 floor vote.

[Sign up for The Daily 202, The Washington Post’s new political tipsheet]

Regardless, the endorsement gives the caucus tremendous leverage to force McCarthy or any other candidate into adopting procedural changes and policy positions favored by conservatives ahead of the decisive floor vote.

“We want rules, policy, process,” said Rep. Dave Brat, the Virginia Republican who ousted ex-Majority Leader Eric Cantor in a 2014 primary. “We want that on paper ahead of time.”

In a statement announcing their endorsement, the Freedom Caucus said “our constituents will simply not accept a continuation of the status quo” and that “under the present circumstances and without significant changes to Conference leadership and process, [Webster] would be best equipped to earn back the trust of the American people.”

In a brief interview Wednesday, McCarthy said he was not concerned about the endorsement.

“I look forward to being able to get their votes,” he said. “My door is always open. Every voice needs to be heard. I’m very confident we’ll all get back together.”

Here's a look at the top candidates vying to replace Rep. John Boehner as speaker of the House of Representatives, Rep. Kevin McCarthy (R-Calif.) and Rep. Jason Chaffetz (R-Utah). (Sarah Parnass/The Washington Post)

McCarthy has struggled to convince a few dozen of the House’s most conservative members that he will not simply continue the policies and practices of Boehner, who has deeply frustrated the party’s right flank.

He appeared Tuesday night before a closed-door forum attended by members of several House conservative groups, including the Freedom Caucus.

“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-Tex.) after leaving the meeting of roughly 60 members. “And I think that is 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.”

But some attendees said McCarthy failed to give the impression that things would change.

“You can’t just say, ‘I’m not John Boehner,'” said Rep. Tim Huelskamp (R-Kan.), the leader of the House Tea Party Caucus. “Well, you really are. How are you different? I wanted specifics. There were very little.”

Huelskamp said he asked McCarthy to make a public statement opposing efforts by the U.S. Chamber of Commerce and other establishment-oriented groups to oppose conservative Republican incumbents who have broken with GOP leadership. McCarthy “would not make that pledge,” he said.

McCarthy has also had to quell an uproar over comments he made in television interviews last week suggesting that a Republican-appointed special committee on the 2012 Benghazi attacks was intended to undermine Hillary Rodham Clinton’s presidential campaign. Those comments emboldened an 11th-hour challenger, Rep. Jason Chaffetz (R-Utah), who says the party needs a “speaker who can speak.”

In late Sept., House Majority Leader Kevin McCarthy claimed credit for the decline in Hillary Clinton's poll numbers because House Republicans created the committee investigating attacks in Benghazi, Libya. He backtracks at a news conference Oct. 7, saying the investigation is not for political gains. (Reuters)

McCarthy addressed the criticism during a Wednesday news conference of House GOP leaders: “I could have said it in a different manner, yes. And I think at any given time, somebody could always say something better. Over time, we’ll prove that we have a very good message.”

Despite the controversy, McCarthy enjoys the support of a solid majority of the 247 member House Republican Conference. But should the Freedom Caucus follow through on its threat to vote as a bloc, it could prevent McCarthy from gaining the majority of all House members, Republicans and Democrats, necessary to claim the speaker’s chair.

Assuming Democrats follow past practice and support their leader, Nancy Pelosi (Calif.), or another Democrat for speaker, McCarthy can afford to lose no more than 29 Republican votes to retain a floor majority.

The Freedom Caucus does not publicize its member roster. But it is believed to contain roughly 35 to 40 members. The group has pledged to vote as a bloc should more than 80 percent of its membership support a particular candidate.

One caucus member, Rep. Ken Buck (R-Colo.), said Wednesday he would not remain in lockstep and would instead support McCarthy.

Webster, a former speaker of the Florida House of Representatives, had courted disaffected conservatives by emphasizing his support for a more inclusive process that would give previously marginalized members a greater say in House affairs.

Rep. John Fleming (R-La.) said Webster’s focus on procedural changes convinced conservatives to back him: “We need to have a voice, we need to have power rather than have the speaker dictate to us.”

It is unclear how many of the Freedom Caucus members would be willing to back McCarthy before the floor vote. Asked after the Tuesday night meeting whether Republicans would unite behind the party nominee, few members pledged outright to do so.

Here's a look at the top candidates vying to replace Rep. John Boehner as speaker of the House of Representatives, Rep. Kevin McCarthy (R-Calif.) and Rep. Jason Chaffetz (R-Utah). (Sarah Parnass/The Washington Post)

“I’ve always been someone in primaries where we duked it out in the primary and we got together in the general,” said Rep. Trent Franks (R-Ariz.). “That’s always been my perspective, but this has some unique twists to it, and I have to at least give whatever these discussions are room to manifest.”

Said Farenthold: “Whoever gets nominated by the conference has got to have the leadership skills to pull together 218 to be able to support him. If he can’t get 218 for himself, it’s going to be a problem.”

Huelskamp did not rule out the possibility that McCarthy might build a solid majority.

“We’ll see,” he said. “I mean, how much does he want this? He’s got three weeks, and I think he’s probably going to need all three weeks. I don’t think Kevin’s the type of guy that going to give up.”