In the Democratic presidential race, Hillary Rodham Clinton is 68; Bernie Sanders, the senator from Vermont, is 74; and the biggest intrigue had been whether Vice President Joseph R. Biden Jr., who turns 73 next week, would join them. (Martin O’Malley, the former governor of Maryland, is the party’s youngest candidate at 52, though he is a major long shot.)

Linking Democratic candidates to Mr. Obama in general, and his health care plan in particular, have long proved winning Republican campaign tactics in many states, but he is hardly the first president to become an election-year burden for some members of his own party. Republicans experienced big losses in 2006 and 2008, many of them attributed to the sagging popularity of President George W. Bush, the economic meltdown and deep concerns about Mr. Bush’s conduct of the war in Iraq. By some measures, Republican losses in Congress under Mr. Bush were larger than Democratic congressional losses under Mr. Obama. And Democrats say Mr. Obama has been successful in building a new Democratic coalition in presidential politics and in mobilizing minority voters.

But even some supporters say that Democrats face a major challenge in cultivating a new generation of politicians able to reach beyond the Democratic base and speak to white voters, especially white men, in states around the country. Bill Richardson, the governor of New Mexico from 2003 to 2011, said he was very worried by the absence of successful Democratic candidates positioned to move up, especially in the South, as well as in swing states like Ohio.

“We are losing the white male vote in droves, and we’ve got to appeal to the white male with stronger economic themes, inequality themes,” he said. “We have to find a way to do that, but what is key is recruiting more white male, and women, candidates. We can’t just become the minority advocate party.”

At a $33,400-a-plate fund-raiser last week, Mr. Obama described a Democratic vision that he said had succeeded in overhauling health care, reviving a moribund economy and making progress on climate change. But he acknowledged the difficulty that Democrats sometimes had in winning over voters.