It is unclear how the House will proceed. Divisions within the Republican caucus have prevented the leadership from presenting a united front or developing a coherent strategy that would keep the government operating and raise the debt limit while extracting demands from the Democrats. House conservatives, encouraged by hard-liners in the Senate like Ted Cruz of Texas, torpedoed a plan by the leadership to tie an increase in the debt ceiling to a laundry list of Republican priorities. They argued that the leadership was pushing legislation that contained too little deficit reduction and undermined the push to gut the health care law.
Republicans are split between moderates who are searching for fig-leaf concession to keep the government open and conservatives who will accept nothing less than a one-year delay in the health care law. Enrollment in the law's new insurance exchanges begins on Tuesday.
"I've been very clear," said Representative Charlie Dent, a moderate Republican from Pennsylvania. "I do not support shutting the government down. I do not support default — under any circumstances."
House conservatives insist that Democrats will give in to their demands rather than defend a health care law that the Republicans say is unpopular with voters in both parties. Sixty-one House Republicans introduced legislation on Friday evening to delay the law, the Affordable Care Act, for one year, and they said they would attach the measure to the Senate spending bill. That voting bloc is large enough to dictate the debate if its members can stick together.
(Read more: Art Cashin: Expect a 'very tough Monday')
"The Democrats realize that we need to delay Obamacare by one year because it's not ready for prime time," said Representative Raúl Labrador, Republican of Idaho. "It's not ready for action,"
But even in the conservative ranks, there is little agreement about the demands that should be made to keep the government open. Social conservatives are seeking to attach language to the next version of a stopgap spending bill that would allow employers and health care providers to opt out of the requirement that insurance policies cover contraception. Representative Chris Smith, Republican of New Jersey, said it "would be unconscionable" to vote for even a short-term spending measure without it.
That has left Senate Democrats exasperated. Senator Harry Reid of Nevada, the majority leader, took a hard line on Friday, saying he would not accept any changes to the health care law, no matter how minor, if they were the price to prevent a government shutdown. He backed that up by announcing that the Senate would meet again on Monday, on the eve of the shutdown, and allow the House to struggle through the weekend.
Senator Charles E. Schumer, Democrat of New York, said there could be no negotiations until House Republicans united around a position.
"They don't yet," he said.
—By Jonathan Weisman of The New York Times