In another political moment, Mr. Obama’s attempt to preserve old governing assumptions might be labeled conservative. But Republicans, even after shifting tactics in the wake of a bracing November defeat, say he will have to fight nonstop to advance his agenda.

“His entire second term on fiscal issues is going to be essentially defensive,” said Representative Tom Cole, a veteran Republican from Oklahoma. “He’s trying to defend not just the New Deal legacy, but also Obamacare.”

Mr. Cole added, “The problem he has is, those programs can’t be defended in their current forms.”

But Republicans also have not made their case for the “structural reforms” that they say have been made urgent by trillion-dollar deficits. In fact, they have failed to do so repeatedly.

In the 1990s, Speaker Newt Gingrich’s attempt to rein in Medicare and Medicaid spending helped Mr. Clinton win a second term. President George W. Bush, after adding a prescription drug benefit to Medicare in 2003, could not persuade a Republican Congress to pass his plan for a partial privatization of Social Security.

In last year’s campaign, the Republican presidential nominee, Mitt Romney, and his running mate, Representative Paul D. Ryan, backed a plan to overhaul Medicare through spending limits on each beneficiary. But their plan pushed such savings 10 years into the future, while they attacked Mr. Obama for having cut Medicare spending to help finance the health care law.

When it comes to Republicans pushing for structural changes in benefit programs, “the record there is not good,” said Peter Wehner, a former Bush White House aide. And the Republican argument will not soon get easier to make.

Mr. Obama acknowledges the need for some cuts in entitlement spending, but he campaigned successfully on higher taxes for affluent Americans as an alternative to the deep cuts that Republicans want. By refusing to negotiate this month over raising the nation’s borrowing limit, Mr. Obama forced Republican leaders to set that cudgel aside without accepting the spending cuts they previously insisted on.