House Democratic leader Nancy Pelosi of California issued a statement saying of the Senate bill that she "will present it to the House Democratic caucus," throwing her support behind the compromise.
Hours before the deadline, Obama, Biden and their aides were at work in the White House, and lights burned in the House and Senate. Democrats complained that Obama had given away too much in agreeing to limit tax increases to incomes exceeding $400,000, far above the $250,000 level on which he campaigned.
A late-night visit to Capitol Hill by Biden helped to convince Senate Democrats to get behind the plan.
"There is a feeling that it's not that this proposal is regarded as great or as loved in any way, but it's a lot better than going off the cliff," said Sen. Chuck Schumer, D-N.Y.
Sen. Dianne Feinstein, D-Calif., called the compromise the "best" that could be done.
ABC News' Matthew Larotonda and John Parkinson contributed reporting.