Democrats, in the majority in the Senate, gave no indication of their plans.
On paper, the two sides are relatively close to an agreement on major issues, each having offered concessions in an intensive round of talks that began late last week.
But political considerations are substantial, particularly for Republicans.
After two decades of resolutely opposing any tax increases, Boehner is seeking votes from fellow Republicans for legislation that tacitly lets rates rise on million-dollar income tax filers. The measure would raise revenue by slightly more than $300 billion over a decade than if all of the Bush-era tax cuts remained in effect.
But Boehner's office trumpeted another figure â¿¿ an estimate that claimed it would amount to a tax cut of nearly $4 trillion compared with what would happen if all those tax cuts were to expire as scheduled with the turn of the year.
Boehner won a letter of cramped support from anti-tax activist Grover Norquist during the day. Norquist's organization, Americans For Tax Reform, issued a statement saying it will not consider a vote for the bill a violation of a no-tax-increase pledge that many Republicans have signed.
But another conservative group came to an opposing conclusion. "Allowing a tax increase to hit a certain segment of Americans and small businesses is not a solution; it is a political ploy," the Heritage Foundation said in a statement.
As for the scheduled defense cuts, Rep. C.W. (Bill) Young of Florida, who heads the House panel with jurisdiction over the Pentagon's budget, said he is undecided how to vote on the legislation.
"This is not a game. This is real because so much of the sequester (spending cuts) would be defense â¿¿ half of it," he said. "I just don't think it's workable."
Rep. Tom Rooney of Florida, a member of the House Armed Services Committee, said he will vote for the legislation even if it leaves the defense cuts in place. He said if he didn't vote for a bill that prevents a tax increase for 99 percent of people "I'm not doing my job."