WASHINGTON — With a budget deal still elusive and a deadline approaching on raising the debt ceiling, Speaker John A. Boehner has told colleagues that he is determined to prevent a federal default and is willing to pass a measure through a combination of Republican and Democratic votes, according to one House Republican.

The lawmaker, who spoke on the condition of not being named, said Mr. Boehner indicated he would be willing to violate the so-called Hastert rule if necessary to pass a debt limit increase. The informal rule refers to a policy of not bringing to the floor any measure that does not have a majority of Republican votes.

Other Republicans also said Thursday that they got the sense that Mr. Boehner, who held two meetings Wednesday with groups of House moderates, would do whatever was necessary to ensure that the country did not default on its debt.

Representative Michael G. Fitzpatrick, Republican of Pennsylvania, was one of just 22 House Republicans this year who helped Mr. Boehner pass three crucially important bills — to avert a fiscal showdown, to provide relief for the victims of Hurricane Sandy, and to pass the Violence Against Women Act — with a majority of Democratic support. He said he expected he might be asked to do so again.

“Hurricane Sandy, the fiscal cliff — all of the big votes require reasonable Republicans and Democrats to come together in order to pass it and get it to the president’s desk,” he said. “This will be no different.”

And, Mr. Fitzpatrick added, “I’ve been there in the past and I’m prepared to be there again.”

Representative Leonard Lance of New Jersey, one of the moderate Republicans who met privately with Mr. Boehner on Wednesday, would not provide details of the meeting, but said, “The speaker of the House does not want to default on the debt on the United States and I believe he believes in Congress as an institution, and I certainly believe he is working for the best interests of the American people.”

Passing a measure with a majority of Democratic votes could bring Mr. Boehner trouble from his right flank. He has so far refused to bring to the floor a measure that could halt the shutdown but that would require significant support from Democrats.

Though not addressing the Hastert rule specifically, a spokesman for Mr. Boehner said that the speaker knew that a default must be headed off.

“The speaker has always been clear that a default would be disastrous for our economy,” said Michael Steel, a spokesman for Mr. Boehner. “He’s also been clear that a ‘clean’ debt hike cannot pass the House. That’s why the president and Senate Democrats should drop their ‘no negotiations’ stance, and work with us on a plan to raise the debt limit in a responsible way, with spending cuts and reforms to get our economy moving again and create jobs.”