FOUR YEARS AGO, Barack Obama became president as the economy was melting down. His election to a second term comes at a calmer but still troubled time. The economy is recovering, but far more slowly than anyone imagined in 2008. The looming fiscal problems the president had vowed to address remain unresolved and, in fact, have deepened after four years of record deficits. After the briefest of celebrations, the president will have to pivot to the looming fiscal cliff of scheduled tax hikes and spending cuts, lest the country veer back into recession.

Still, the prospect of four more years offers Mr. Obama a chance to conserve the accomplishments of his first term and to complete its unfinished work.

The accomplishments, as we said in endorsing Mr. Obama for reelection, include the stabilization of the economy and health-care reform. The latter has, for the most part, not taken effect; a second-term task will be to ensure that it achieves the dual goals of extending coverage to millions of uninsured Americans and beginning the difficult, uncertain process of restraining the unsustainable rise of health-care costs.

But the real measure of Mr. Obama’s success, and the ultimate assessment of his presidential tenure, will be in whether, in a second term, he can fulfill some of the promise that made Americans so excited about his candidacy four years ago. Will an Obama second term allow him to transcend the ideological divides that he vowed to bridge but instead found so daunting?

That is a tough order in a partisan age and with a divided, gridlocked Congress; there is no indication that the intransigence Mr. Obama encountered from the opposition party will diminish. But Mr. Obama has had four years of seasoning; one question is whether he can demonstrate the political canniness and legislative finesse that too often eluded him during the first term.

Perhaps more important is whether Mr. Obama will demonstrate more willingness — more bravery, actually — to take on issues he ducked the first time around: reforming entitlements, particularly Medicare, and reducing the unsustainable debt. Mr. Obama’s promise of a balanced, long-term combination of spending cuts and tax increases is the correct one. He will have to bring his own party along on entitlement reform, and persuade a dug-in Republican Party of the need for increased tax revenue not based on the wishful assumption of faster economic growth.

There are other important pieces of unfinished business, here and abroad. At the top of the list are comprehensive immigration reform, an enterprise that Republicans would be wise to join if they hope not to be made obsolete by changing demography, and climate change, whose toll may be revealing itself in the extreme weather patterns of recent years. Overseas, the Iranian nuclear program will pose a fateful challenge, possibly within months. Mr. Obama will have to ensure that gains in Afghanistan and Iraq are not erased in the aftermath of U.S. troop withdrawals. His dithering in Syria as 30,000 civilians have been massacred is a particular blot on his first-term record, one for which he could begin to make amends in the second.

On election eve four years ago, we celebrated, along with Americans of both parties, that a black American could be elected president and hoped, again like many Americans, that a young, charismatic leader could help heal partisan divides and confront the difficult choices that politicians generally would rather duck. Mr. Obama’s victory Tuesday felt less momentous, but it allows him the opportunity to fill in the blanks of a still uncertain legacy.