The Senate on Monday rejected a House resolution that would have funded the federal government until Dec. 15 but delayed implementation of Obamacare for one year.
The measure now returns to the House, where Republicans are meeting privately to determine what to do next.
Senate leaders also warned the House GOP against using very short-term budget bill — those that fund the government for 10 days or less — to buy more time, even if the short-term bill leaves Obamacare untouched.
Senate Majority Leader Harry Reid, D-Nev., called on the House to take up the original Senate resolution, which funds Obamacare. It would pass on the House floor with Democratic support, Reid said.
"They are spinning their wheels," Reid said. "We are not going to change Obamacare."
He called the GOP maneuvers "a fool's errand."
Many conservatives want to amend the stopgap government funding bill in a way that defunds all or part of the new health care law. Just hours before the midnight deadline, Senate Democrats were pledging to reject any measure that touches the health care law, even if it leads to a shutdown.
The 54-46 Senate vote on the budget bill fell directly along party lines, but Republicans are divided internally.
More conservative members want the GOP to keep passing measures that diminish the impact of the health care law and then blame Democrats for a shutdown that might result if they don't pass the House version.
More senior and moderate Republicans, however, want to abandon the Obamacare defunding effort because it's clear Democrats will continue to reject any bill that includes it.
Republicans tend to get blamed for shutdowns, polls show. And the latest CNN/ORC International survey shows 46 percent of respondents would blame the GOP.
"We are not going to repeal Obamacare," Sen. John McCain, R-Ariz., said just after the Senate rejected the latest House proposal Monday. "We may do this for a day, we may do it for a week. But it is going to end up the same way."
Reid suggested he would reject any resolution that funds the government for just a few days, as some Republicans are privately proposing.
"Ten days at a time, not so good," Reid said, adding that the Senate bill, which funds the government until Nov. 15, is short enough.