House Speaker John A. Boehner is facing increasing pressure as several rebellious Republicans hinted that they won’t vote to re-elect him to run the chamber, and a conservative interest group announced a bid to recruit someone else to run against him for the speakership.

Mr. Boehner, an Ohio Republican, is not in any danger yet — the rebellion shows no signs of reaching beyond a small group of dissatisfied lawmakers — but it could complicate his efforts to strike a deal with President Obama to head off the looming “fiscal cliff” that will send tax rates soaring and will impose automatic spending cuts early next month.

American Majority Action, a conservative interest group, on Monday endorsed Rep. Tom Price and two other Republicans who they said should replace Mr. Boehner and his top lieutenants, and has launched a lobbying push to try to sway rank-and-file members to withhold their votes from Mr. Boehner.

Mr. Price won’t challenge Mr. Boehner, a spokesman said.

But lawmakers can vote for anyone when the House members cast ballots Jan. 3 for the next speaker, and if Republican members vote for someone other than Mr. Boehner, that could help Minority Leader Nancy Pelosi, California Democrat.

So far it’s a matter of threats, as some Republicans hold out the possibility of voting for an alternative.

Last week, Rep. Justin Amash, a Michigan Republican who was one of four lawmakers booted from his committee assignments after leaders said he wasn’t a team player on votes, refused to commit to supporting Mr. Boehner. He told CNN that the speaker needs to be “willing to make amends.”

On Monday, Rep. David Schweikert of Arizona, another Republican who was stripped of his assignments, seemed to float the idea of voting for Rep. Eric Cantor of Virginia, who is the second ranking Republican in the House.

“I must tell you that I’ve had wonderful relationships with [House Majority Leader] Eric Cantor and I’ve actually found him to be one of the truly straight shooters I’ve dealt with,” Mr. Schweikert said on MSNBC’s “Morning Joe.”

Asked specifically whether he would vote for a Speaker Cantor, he paused.

“You know, it’s bad enough being removed from your committee — I’d actually like not to be chairman of janitorial supplies if I answer that,” he said.

“I didn’t come to Washington to fight against my Republican colleagues, or even against my colleagues on the other side of the aisle,” he wrote in a commentary published in The Washington Times on Tuesday. “I came to Washington to fight for the values that make our country unique — for the economic freedom that gives life to the American Dream. I came to fight for the people back home who still can’t find a job, for the families who worry about their children and grandchildren’s futures. No matter the price, that is what I intend to do.”

Another of the targeted lawmakers, Rep. Tim Huelskamp of Kansas, said Monday that he has formally asked Mr. Boehner to be reinstated to the House Agriculture and Budget committees.

Mr. Huelskamp, along with Mr. Amash and Mr. Schweikert, also wrote to Mr. Boehner asking for a complete written explanation as to why they were removed from their committee assignments, plus any purported voting “scorecards” used to make the decision. Mr. Amash was removed from the House Budget Committee and Mr. Schweikert from the House Financial Services Committee.

Mr. Boehner’s office responded to the request from the three congressmen, but a spokesman said Mr. Huelskamp will not be reinstated to his committees.

The spokesman had no comment on Mr. Price’s decision not to raise a challenge for the speakership.

Conservative interest groups have complained about the committee moves and Mr. Boehner’s negotiations in the fiscal cliff talks.

Mr. Boehner and his lieutenants have said they would be willing to accept $800 billion in higher income taxes for the wealthy, as long as the money comes from eliminating deductions and loopholes, not from raising rates.

That runs against conservative orthodoxy, which holds that the deficit is a result of too much spending, not of too little taxing. Mr. Obama, though, has insisted that higher rates be the centerpiece of any final deal and that the wealthy can afford to pay more in order to maintain the promises the government has made to lower- and middle-income Americans.

As he tries to negotiate, Mr. Boehner has the support of the rest of House leadership. Even many rank-and-file members who aren’t enamored with his opening offer say he still has their backing as he tries to negotiate a deal.

Committee assignments are doled out by a steering committee headed by Mr. Boehner, and his spokesman, Michael Steel, said those decisions are “based on a variety of factors.”

Leadership aides disputed the notion that the four Republicans who were kicked off their committees were punished for being too conservative. They pointed to conservative lawmakers who won key committee assignments this year as evidence that it wasn’t a purge.

Party leaders often struggle to maintain discipline. Earmarks once were a key tool, as leaders doled out spending for local projects based on who was most cooperative, but with the end of earmarks, leaders have fewer tools at their disposal. Committee assignments are one way to punish lawmakers.

Rep. Walter B. Jones of North Carolina, who was booted from the Financial Services Committee, said he has no regrets and vowed to continue to vote his conscience.

“I’m not going to sacrifice my integrity for anyone or any party,” Mr. Jones said. “It’s the price you pay. I didn’t come up here to be a puppet for anyone. And I think the public back in my district, which is the most important, has seen I’m willing to do what I think is right.”

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