That consensus suggests that the odds of an economy-damaging stalemate are relatively low, despite rising jitters in the capital. Yet everything else about how the White House and Congressional negotiators will try to strike a deal, and then coax majorities to approve it, remains opaque.
“Even those of us quite close to it have a hard time saying how the movie ends,” said Representative Chris Van Hollen of Maryland, the ranking Democrat on the House Budget Committee.
The showdown encompasses three interlocking fiscal disputes that will challenge Mr. Obama and his Republican interlocutors to bridge seemingly irreconcilable goals.
Perhaps easiest to resolve is the effort by some conservative Republicans to eliminate financing for the new health care law in return for keeping the government open beyond Sept. 30, the end of the fiscal year. As expected, Mr. Obama is unyieldingly opposed to undercutting his signature domestic policy achievement.
The House Republican leader, Eric Cantor of Virginia, has already rejected the Republican strategy as doomed to fail. Most Senate Republicans have not signed on, and Senator Richard M. Burr of North Carolina has called it “the dumbest idea I’ve ever heard.” Even one supporter, Senator Rand Paul of Kentucky, recently suggested that the threat was simply a tool to provoke negotiations.
A second challenge is determining the fate of the across-the-board budget cuts known as the sequester if Congress avoids a shutdown by extending government financing.
Republicans remain adamant that the level of budget cuts required by the sequester, about $90 billion per year, be continued. But with increasing complaints about the effects of those cuts on the Pentagon and elsewhere — shown by House Republicans’ inability to pass their own transportation spending bill last month — some party leaders want to rearrange the burden of those cuts so they fall instead on entitlement programs like Medicare and Social Security.
The White House and Congressional Democrats, however, rule out that trade, except as part of a larger long-term deal that also includes new tax increases. And Republican resistance to tax increases, which has precluded such a “grand bargain” in recent years, has stiffened since the Bush tax cuts for top-earning Americans expired at the end of 2012.
The third challenge may be the most worrisome. While the sequester pinches particular constituencies, and a government shutdown would inconvenience millions, economists warn that a default resulting from a failure to raise the government’s debt limit could tip the economy back into recession.
That challenge also appears, at least on the surface, the most intractable. Speaker John A. Boehner of Ohio has reiterated that Republicans will not raise the debt limit without offsetting spending cuts.
Mr. Boehner’s demand would require fewer cuts than during the 2011 debt crisis, when the debt ceiling needed to rise by about $110 billion per month to avoid default. That amount has shrunk to around $70 billion, according to the Bipartisan Policy Center, because the top-end tax increases and revenue from a stronger economy have helped shrink the deficit substantially.
But Mr. Obama, burned by the downgrade of the United States debt rating after those 2011 negotiations, insists he will not negotiate on the issue this time. It is as imposing a fiscal puzzle as veterans of Washington budget fights have seen in years.
“This is, for me, very, very difficult to figure out,” said Stephen Bell, a longtime Senate Republican budget aide now at the Bipartisan Policy Center.
No formal negotiations have begun, although the White House chief of staff, Denis R. McDonough, has been meeting with a few Senate Republicans in search of common ground.
Congressional aides have also started exploring potential stopgaps. They begin with a temporary extension of government funding to allow budget talks to continue through year’s end.