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“He was excited and thought it was the best opportunity for him to address the grassroots on an important subject,” Ms. Kukowski said.

Mr. Boehner, who holds a 87 percent lifetime conservative rating with the American Conservative Union, used his CPAC speech four years ago to talk about the GOP relationship with the emerging tea party movement and praised it as an engine that could drive Republicans.

“The Republican Party should not attempt to co-opt the tea parties,” Mr. Boehner said at CPAC 2010, after being introduced to a standing ovation. “I think that is the dumbest thing. What we will do as long as I am leader is respect them, listen to them and walk amongst them.”

Since then, though, the relationship has been rocky, in part reflecting Mr. Boehner’s conflicting duties as a top GOP figure and the man who must maintain operations on Capitol Hill.

After some spending and debt fights led to GOP victories, Mr. Boehner and his lieutenants have increasingly locked horns with his party’s right flank over the best tactics for advancing conservative policy goals.

A battle last fall over whether to tie a spending deal to a fight over defunding Obamacare ended up in a government shutdown. Although polls showed the Republican Party’s image was tarnished, Mr. Cruz — who pushed to link Obamacare and the spending bills — has become more popular among grass-roots conservatives.

Mr. Boehner’s frustration with limited-government groups — including Heritage Action and the Club for Growth — boiled over at a December press conference, where he said those attacking the bipartisan budget deal that Rep. Paul Ryan, Wisconsin Republican, negotiated had “lost all credibility.”

Last month, tea partyers slammed Mr. Boehner for giving in to Democrats’ demands for an unconditional increase in the federal debt ceiling. Tea party Republicans refused to sign off on any deal. The speaker was forced to turn to Democrats for the votes to pass the borrowing increase that President Obama wanted.

Tea partyers now are looking to remove Mr. Boehner from the top House job.

Tea Party Patriots, led by CPAC speaker Jenny Beth Martin, started a “Fire the Speaker” petition that has almost 93,000 signatures.

The Tea Party Leadership Fund announced last week that it is backing a high school teacher, J.D. Winteregg, against Mr. Boehner in Ohio’s May 6 primary election.

Mike McKenna, a Republican Party strategist, said Mr. Boehner’s opponents should be careful what they wish for.

“In about two years, folks on the right are going to be complaining about whoever the next speaker is and remembering Boehner fondly,” Mr. McKenna said. “They are angry at the world. For some reason, they have focused some of this anger at Boehner. I have no clue why.”