WASHINGTON — In some ways, the partisan standoff over looming budget cuts resembles earlier links in the chain of fiscal battles that began two years ago.

But the politics of one core dispute between Democrats and Republicans — what to do about Medicare — are changing. And some of those changes complicate President Obama’s agenda, even as he continues to flex his postelection muscle.

One shift is the shrinking magnitude of the Medicare spending problem — a consequence, at least for now, of a recent slowdown in the rise of health care costs. That diminishes the willingness of Congressional Democrats, and perhaps the administration, too, to accept the sort of Medicare curbs that Mr. Obama has indicated that he favors.

Another is a moderation in the public stance of Republican leaders. In recent weeks, they have advocated smaller changes to Medicare than the “premium support” or voucher plan that Mitt Romney advocated and that Mr. Obama denounced in last year’s presidential campaign.