All agree that he does work hard, and is truly engaged by his work. CBS Radio's Mark Knoller keeps track of presidents' comings and goings. This past May, he said Obama had spent all or part of 54 days at the Camp David presidential retreat in Maryland. At the same point in his first term, George W. Bush had been there for all or part of 256 days.

This is not to say that Obama is averse to regular-guy moments of fun, like a quick trip to a burger joint with the vice president. He remains an ardent basketball fan. He startled an audience at a fundraiser at Harlem's Apollo Theater by breaking into a few bars of Al Green's "Let's Stay Together."

But the informal Obama is not necessarily convincing. When white police Sgt. James Crowley arrested black Harvard professor Henry Louis Gates as he tried to get into his own home and charged him with disorderly conduct, Obama said Crowley had "acted stupidly." (He later would say the phrase was ill-chosen.) To settle the issue, Obama held a "beer summit," inviting Gates and Crowley to come to the White House for a few brewskies. The event was lampooned: "This could be trouble, because the last time Obama got a few beers in him, he bought General Motors," said comedian Conan O'Brien.

Mostly, he remains a dignified and graceful figure — graying, like many of his predecessors, under the weight of office. He is, at heart, a dad, and Brinkley thinks that is one of the reasons his popularity ratings remain high.

"His strongest suit may be in the end that he is such a tremendous husband, a tremendous father," says Brinkley. "Even his mother-in-law lives in the White House."

There's also first lady Michelle Obama; and 11-year-old Sasha and 14-year-old Malia; and there is Bo, the Portuguese water dog the girls were promised as a reward for leaving Chicago to move to the executive mansion.

Obama's fatherly impulses have surfaced at many of the most painful moments of the past four years. When he visited the victims of the shootings in Aurora, Colo., and their survivors, he said he was doing so as a "father and as a husband." And after the killing of a black teenager, Trayvon Martin, by neighborhood watch volunteer George Zimmerman in Sanford, Fla., Obama spoke not only of his feelings as a parent, but as a man who understood firsthand the possible consequences of skin color:

"If I had a son, he'd look like Trayvon."

No other president could have said those words.