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In 2011, during the first debt fight of his tenure, he won a deal that has cut overall spending for two consecutive years — the first time that has been achieved since 1950.

Since that peak, though, Republicans have struggled to win concessions on three successive debt votes and has reversed its push against spending. Indeed, December’s budget deal offset some of the cuts Republicans won in the 2011 budget agreement.

On Tuesday, Republicans said they were left with little choice.

With so many Republicans opposed to any debt increase, leaders were unable to come up with the votes to pass a plan that would halt parts of Obamacare or build the Keystone XL pipeline in exchange for a debt increase.

Most of the 28 Republicans who voted in favor of the clean debt increase were leaders, chairmen of committees or members of the Appropriations Committee.

Rep. Tom Cole, an Oklahoma Republican who voted against the debt increase, said Mr. Boehner had no options, but he added that the result of agreeing to a third straight increase with no major cuts attached is that Republicans lose leverage in any future debt negotiations.

“I understood the previous times, but I think we’re slipping into a bad habit,” he said. “I’m not here condemning people for what they did — they’ve done it to try and deal with the immediate situation, but I think long term, we need to rethink how we do it and a lot of Democrats would like to get rid of the whole debt ceiling idea altogether. I think that’s a mistake, personally.”

Mr. Obama and congressional Democrats remained united throughout the battle for a clean debt increase. That left Mr. Boehner with no negotiating partner and no offer of his own.

“We don’t have 218 votes. And when you don’t have 218 votes, you have nothing,” the speaker told reporters ahead of the vote, explaining his lack of leverage.

Just a single Republican — Ways and Means Committee Chairman Dave Camp of Michigan — spoke during the floor debate.

Most Republican lawmakers seemed eager to move on and saw the vote as a way to “clear the decks” of a thorny political problem and resume attacks on Obamacare and Mr. Obama’s other policies.

Democratic leaders were eager to debate the bill. House Minority Leader Nancy Pelosi of California said it proved that Democrats were the ones interested in upholding the Constitution’s directive that the validity of the debt never be questioned.

“The full faith and credit of the United States of America is not in doubt,” Mrs. Pelosi said.