Senator Ted Cruz, Republican of Texas, immediately began encouraging House conservatives to stand up to any move by Republican leaders to back off efforts to gut the health care law. He had been urging his Senate colleagues all week to oppose ending debate as a way to force Democrats to accept language defunding the Affordable Care Act. But with the clock ticking toward a shutdown, an overwhelming bipartisan majority wanted to act quickly to move the spending bill back to the House.

The Senate legislation would almost certainly win approval, largely with Democratic votes, if it was put to a vote in the House, but conservatives warned that it could hurt the beleaguered speaker dearly if he took that step.

“I think it would be devastating to the speaker’s support,” said Representative Richard Hudson of North Carolina, one of the members urging the Republican leadership to drive a hard bargain with the Senate.

“I think the question is, Do we go with the carrot or the stick strategy?” Mr. Hudson added. “Do we try to do something bad enough to force Harry Reid to negotiate with us, or do we do something that we think he can’t refuse?”

Republicans may also consider a simple bill to keep the government open for as little as seven days while the legislative jousting continues. That was sternly opposed by senior Republicans, like Representative Harold Rogers of Kentucky, the chairman of the House Appropriations Committee.