But foreign policy, a natural palliative for legislative blues, offers the commander-in-chief other outlets. Reagan signed a major arms control treaty with Mikhail S. Gorbachev, the last president of the Soviet Union, and Mr. Clinton shepherded a peace deal in Northern Ireland.

Mr. Obama is disengaging the United States from long, unpopular wars in the Middle East — and resisting Congressional pressure for greater American intervention in Syria — while elevating engagement with China and other Asian nations.

Domestically, politically weakened presidents can use executive powers to bypass uncooperative lawmakers. Mr. Clinton proved especially assertive in using executive orders. Mr. Obama aims to do that now on climate change without suffering the sort of reversal Mr. Clinton did in 2001, when Mr. Bush and a Republican Congress rolled back Mr. Clinton’s union-backed regulations on workplace safety.

Recalibrating already established policies can be at least as important as new victories. Mr. Bush adjusted his war policy in his second term with a surge of new troops to Iraq, a decision that in part reduced violence enough, Mr. Beschloss said, that historians may alter their judgment of the conflict. The durability of Mr. Obama’s landmark achievement on health care may in turn depend on whether Americans see its carrying out over the next years as a success or a failure.

Like all second-term presidents, “Obama’s got to fine-tune,” said Dr. Brinkley, who with Mr. Beschloss is part of a group of historians that meets occasionally with Mr. Obama to offer perspective. “Policy is about two years behind the selling of it.”

By historical standards, some circumstances augur well for the incumbent. Eisenhower and Mr. Bush oversaw weakening economies in their second terms compared with a slowly improving economy for Mr. Obama, though unemployment remains high.

Presidential health is another factor. Eisenhower had a mild stroke in his fifth year and Reagan had colon surgery, but Mr. Obama appears vigorous. His political health, if not exactly robust, with approval ratings below 50 percent, remains untouched by any hint of personal scandal.