Mr. Boehner and Mr. Reid issued their own joint statement after the meeting on Thursday night, saying that they and their advisers would “continue to work through the night to attempt to resolve our remaining differences.” Negotiators went to work in the Capitol, though top aides expressed pessimism about a quick conclusion.

After the meeting, Mr. Obama canceled a planned trip to Indiana on Friday to participate in the final push to get an agreement.

Throughout the day, members of both parties played a game of chicken, seeking to force the other to give in as the deadline of midnight Friday approached. Mr. Boehner in particular faced a tricky calculation about how much he could compromise without losing support not just from his large contingent of Tea Party-inspired fiscal conservatives, but also from social conservatives who were eager for a victory on abortion and other issues.

As Mr. Reid returned from the White House and briefly took the Senate floor, he said that the issues dividing the Senate and House were “extremely narrow,” but that it was far from certain they could be worked out in time.