WASHINGTON  The day before Joseph R. Biden Jr.’s birthday last week, Barack Obama surprised him after lunch with candlelighted cupcakes. Within hours, the photograph of the president-elect and his running mate, smiling over the dessert, was on the evening news.

The photograph, circulated by Mr. Obama’s office, was meant to project unity, confidence and camaraderie. But while Mr. Obama has moved quickly to assemble his White House staff and the beginnings of a cabinet, he is lagging behind even the chronically late President Bill Clinton in bringing clarity to the role his vice president will play.

So far, Mr. Biden has not been given a defined portfolio, the way Al Gore was given the environment and technology in 1992. And Mr. Obama’s aides say they do not expect Mr. Biden to assume the kind of muscular role that Vice President Dick Cheney has played over the last eight years, although he is expected to put out a number of fires.

“I’m sure that there will be discrete assignments over time,” said David Axelrod, a senior adviser to the president-elect. “But I think his fundamental role is as a trusted counselor. I think that when Obama selected him, he selected him to be a counselor and an adviser on a broad range of issues.”