WASHINGTON — The latest federal budget showdown has quickly set the stage for the next one, as Republicans and Democrats have just three months to craft a new agreement to avoid another shutdown crisis.

This time, though, the parties come to the table with serious incentives to reach a deal. Both want to make changes to mandatory budget cuts that kick in next year, slicing into Pentagon accounts that Republicans want to protect, and domestic programs, such as Head Start early education classes, that Democrats favor.

But don't expect the kind of "grand bargain" once pursued by President Obama and House Speaker John A. Boehner (R-Ohio). Rather than a sweeping deficit-reduction plan, any deal crafted by the Dec. 13 deadline that Congress set is likely to be far more modest.

Interest in a big fix for the nation's budget has faded among Democrats because many no longer believe it is necessary or worth the political perils. The deficit has declined rapidly, and the national debt, now $16.7 trillion, is projected to be stable or even declining as a share of the economy well into the next decade.

For Republicans, the idea of cutting expensive programs for retirees draws support from many party leaders, but divides the rank and file. The GOP has grown much more dependent on the votes of Americans older than 65 and on lower-income whites, groups that want to preserve Social Security and Medicare.

Although the politics have shifted as the battered GOP struggles to regroup amid deep internal divisions, the nation's budget problems remain difficult and economically daunting: The country is on a budget trajectory that, while substantially improved from the recent recession, remains unsustainable.

Yet neither party appears to have the political motivation to make far-reaching changes to tax policy and safety net spending that economists say is needed for long-term fiscal health.

Rep. Paul D. Ryan (R-Wis.), the House Budget Committee chairman whose views on federal spending carry substantial weight with fellow Republicans, has called for a more modest "down payment."

Sen. Patty Murray (D-Wash.), the seasoned Senate Budget Committee chairwoman, said, "We're going to look at everything in front of us."

Over a breakfast of bagels and pastries, Ryan, Murray and other members of a new joint House-Senate committee charged with crafting a budget deal met for the first time Thursday — the day after the president signed the agreement that ended the recent standoff.

That episode shut down government for 16 days, threatened a debt default and cost tens of billions of dollars. The deal reached by Democrats and Republicans funded the government through Jan. 15 and suspended the debt limit until Feb. 7.

"Our goal is to do good for the American people — to get this debt under control, to do smart deficit reduction, and to do things that we think can grow the economy and get people back to work," Ryan said.

Murray said, "It's going to be a challenge, but we believe we can find common ground."

At issue is almost $100 billion in automatic cuts to the more than $3-trillion federal budget in the new year — on top of similar across-the-board reductions that kicked in earlier this year.

Those so-called sequester reductions — which were agreed to after a 2011 debt-limit standoff between Obama and House Republicans — have been the GOP's greatest victory in the budget battles. They hewed closely to Boehner's doctrine to offset every $1 increase in the debt with cuts.

That approach, though, quickly became politically unsustainable, as even Republicans balked over slashing defense and infrastructure spending.

But Republicans want to prevent reductions to Pentagon accounts, while Democrats want to protect education and social programs. These core differences have divided the parties historically and, in recent years, fueled by the GOP's tea party flank, led to the cycle of brinkmanship that defines Washington's budget talks.

Ryan has proposed doing away with some cuts by raising revenue from safety net programs — for example, asking wealthier seniors to pay more for Medicare, something Obama has also considered.

Sen. Bob Corker (R-Tenn.), who has emerged as a key broker in budget matters, called the 2011 Budget Control Act agreement "the single best vote [he's] had in the United States Senate."

"It can be even better," he said last week. "We can substitute some of the sequester for more thoughtful reductions, and hopefully we will do that in the next three months."