As the Senate announced there would be no further floor votes for the evening, the House was beginning its work.
Boehner was convening a closed-door meeting of rank-and-file House Republicans, whose reluctance to support a tax hike has been a critical issue in previous attempts to reach a deal.
Divisions within the GOP have left Boehner on the sidelines in the final round of talks, and he is expected to bring only part of his majority along for any agreement. Support from House Democrats, under Minority Leader Nancy Pelosi of San Francisco, will play a greater role in the final deal.
Democrats have not been pleased with the narrowing definition of the wealthy for tax hikes, but many said they were willing to support a compromise.
Lawmakers appeared embarrassed at times over the state of affairs Sunday as tourists milled about the Capitol, with several senators saying they were talking among themselves about alternatives should the leaders fail.