"I don't think that any reasonable person thinks there's anything to be gained by a government shutdown," Sen. John Cornyn, R-Texas, said. "Rather than a shutdown of government, what we need is a Republican victory in 2014 so we can be in control. I'm not sure those are mutually compatible."
House leaders intended to set a vote for Friday.
GOP leaders telegraphed that they would likely concede to the Senate's demand for a stopgap spending bill shorn of the Obamacare provision but that they would carry on with the fight on legislation to increase the government's borrowing cap.
"There should be no conversation about shutting the government down," House Speaker John Boehner, R-Ohio, said. "That's not the goal here."
The debt-limit measure, required to allow the government to pay all of its bills on time, would be brought to the House floor as early as next week and would allow the Treasury to borrow freely for one year.
Republicans vow to load that bill with a GOP wish list, including another assault on Obamacare and a provision to force the construction of the Keystone XL pipeline from Canada to Texas Gulf Coast refineries, a project that environmentalists oppose and that the Obama administration so far has refused to approve. Other elements will reflect different Republican budget priorities, including as-yet-undisclosed savings from health care and government benefit programs and steps to speed work on an overhaul of the tax code.
Democrats strongly denounced the Republican move. Sen. Chuck Schumer of New York said the GOP was pursuing an "insane plan." Sen. Amy Klobuchar of Minnesota said, "A group of extremists is threatening to hold our government hostage."
Obama, speaking Wednesday to business executives at a meeting of the Business Roundtable, said, "You have never seen in the history of the United States the debt ceiling or the threat of not raising the debt ceiling being used to extort a president or a governing party and trying to force issues that have nothing to do with the budget and have nothing to do with the debt."
Separately, the Obama administration's budget director, Sylvia Burwell, issued a memo to department heads that said, "Prudent management requires that agencies be prepared for the possibility of a lapse" in funding.