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.”