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“I don’t sense much in the way of organized opposition,” he said. “There will be plenty of conservatives supporting the speaker. It won’t be that kind of split.”

Mr. Cole pointed out that it was Mr. Boehner who was at the party’s helm when it took control of the chamber in 2010 and maintained that majority in the 2012 elections. “I think the reserve of good will for him is very, very deep,” he said.

After the meeting, Mr. Cole said the speaker was not asking members for their votes during it — which would have been a possible sign of insecurity or fear of rebellion — and added that he’d be “shocked” if a “significant number” of Republicans didn’t vote for Mr. Boehner.

“This is a very diverse conference — a lot of strong opinions and a lot of principled people, and so there’s going to be differences from time to time. But John Boehner manages it exceptionally well, and I just don’t sense a large-scale dissatisfaction with his leadership,” he said.

Still, Mr. Boehner felt more wrath from some in his party after he sent lawmakers home Wednesday without passing an emergency spending bill for Superstorm Sandy relief.

Republicans from New York and New Jersey blasted him for the move, and one, Rep. Peter T. King, even told wealthy New York donors not to contribute to the party.

Rep. Michael G. Grimm, who represents the hard-hit area of Staten Island, voted for the cliff deal Tuesday and praised Mr. Boehner for his leadership immediately after the vote.

But by Wednesday morning, when it was clear that a vote for Sandy aid would not come up, Mr. Grimm laced into the speaker in a floor speech and considered not voting for him Thursday.

After a meeting Wednesday afternoon, Mr. Boehner and Mr. Cantor said passing Sandy spending would be a top priority for the new Congress, and the lawmakers from the Northeast said Mr. Boehner would retain their support.

Mr. Boehner also took heat after several conservatives were booted from their committee assignments ahead of the new Congress.

Leadership aides said the men were ousted because they weren’t team players, but the lawmakers and outside pressure groups said it seemed they were being punished for their conservative voting records.

Rep. Tim Huelskamp, Kansas Republican and one of the members who lost a committee spot, was coy when asked whether he would vote for Mr. Boehner for speaker.

“We’ll find out tomorrow,” he said Wednesday evening as he ducked back into the conference meeting.

Sean Lengell contributed to this report.