“Will this deliberative body, whether it is the greatest in the world or the worst in the world, go ahead and decide on this issue, so we can at least tell the American people we are going to do what we haven’t done for four years and what every family in America sooner or later has to do — and that is to have a budget?” he asked. Although few of Mr. McCain’s colleagues took to the floor to join him, many have expressed similar views.

Senator Roy Blunt of Missouri, a member of the Republican leadership, said that at this point, resistance had to give.

“I suspect senators have held back long enough on the decision to go to conference,” he said.

Republicans who have made the deficit their central ideological focus are, in some sense, the dog that caught the bus. The nonpartisan Congressional Budget Office estimated this month that the deficit for this fiscal year, which ends Sept. 30, will fall to about $642 billion, or 4 percent of the nation’s annual economic output, less than half the 2011 deficit and about $200 billion lower than the agency had estimated three months ago.

The agency forecast that the deficit, which topped 10 percent of the gross domestic product in 2009, could shrink to as little as 2.1 percent of the G.D.P. by 2015, a level most analysts say would be easily sustainable over the long run.

And a conservative stamp is hitting the government, thanks to the across-the-board spending cuts known as sequestration. On Friday, 115,000 employees at the Internal Revenue Service, Environmental Protection Agency, Department of Housing and Urban Development and the small Office of Management and Budget — 5 percent of the federal work force — stayed home on unpaid furlough.

House Republicans had envisioned a plan to reach a comprehensive deficit reduction deal predicated on a showdown in July over the debt ceiling. That showdown was supposed to drive both sides back to the bargaining table, but a rapidly falling deficit, rising tax payments and huge infusions of cash from the newly profitable, federally controlled home financing agencies Fannie Mae and Freddie Mac have scrambled those plans. Now, the debt ceiling may not have to be raised until October or November, in the next fiscal year.

Before then, unless a budget deal can be struck, Congress must pass bills to finance the government based on very different guidelines in the House- and Senate-passed plans. The House Appropriations Committee will have to draft a bill financing labor, health and education programs at $121.8 billion, a 19 percent cut from current levels even after the across-the-board cuts took effect. The bill to finance the Interior Department and Environmental Protection Agency cannot exceed $24.2 billion, down 15 percent from the current levels after the cuts.