Mr. Boehner, who faces a re-election vote on his post on Thursday when the 113th Congress convenes, had grave concerns as well, but he had pledged to allow the House to consider any legislation that cleared the Senate. And he was not eager to have such a major piece of legislation pass with mainly opposition votes, and the outcome could be seen as undermining his authority.

Adding to the pressure on the House, the fiscal agreement was reached by Senator Mitch McConnell of Kentucky, the Senate Republican leader, and had deep Republican support in the Senate, isolating the House Republicans in their opposition. Some of the Senate Republicans who backed the bill are staunch conservatives, like Senators Patrick J. Toomey of Pennsylvania and Tom Coburn of Oklahoma, with deep credibility among House Republicans.

The options before the House Republicans were fraught with risks. Senate Democrats said they would not brook any serious amendments to their bill — one that was hard fought and passed in the dark of night with many clenched teeth on either side of the aisle. Senate Democratic leaders planned no more votes before the new Congress convenes Thursday afternoon.

An up-or-down House vote on the Senate measure presented many Republicans with a nearly impossible choice: to prolong the standoff that most Americans wished to see cease, or to vote to allow taxes to go up on wealthy Americans without any of the changes to spending and benefit programs they had fought for vigorously for the better part of two years.

“I have read the bill and can’t find the spending cuts — even with an electron magnifying glass,” said Representative Trey Gowdy of South Carolina. “It’s part medicinal, part placebo, and part treating the symptoms but not the underlying pathology.”