That leaves Social Security, the other big entitlement benefits program and one that Mr. Obama has suggested in the past that he is willing to tackle. While its looming problems are not of the scale of those afflicting Medicare, it now stands as the likeliest source of the sort of large savings needed to bring projected annual deficits to sustainable levels, many budget analysts agree.

And, they say, packaging future reductions in the retirement program that Democrats zealously defend with tax increases that Republicans typically oppose would have the makings of a grand compromise to shrink the debt.

“You would think that there ought to be a way to get together and talk about a balanced package of some changes in benefits and some increases in revenues that would actually help Social Security,” said James R. Horney, the director of federal fiscal policy at the Center on Budget and Policy Priorities, a liberal-leaning research organization.

Some liberals, however, already have begun mobilizing to oppose any changes to Social Security benefits, arguing that the program does not face an imminent crisis. A group called Social Security Works began forming in January, with financing from Atlantic Philanthropies, and is seeking alliances with other groups.