Biden mentioned neither the president nor Obamacare in more than 20 minutes of remarks. Nor did he note, as some other speakers did, how the alliance of the president and Democrats in Congress had stared down the tea party to reopen the government.

Instead, sounding like a man who has not given up the ghost of presidential ambition, Biden linked his own story of middle-class economic struggle with that of McAuliffe, a fellow Irish American who grew up in an unassuming Syracuse, N.Y., neighborhood without money or connections.

Recalling that he had attended law school in Syracuse, and that he knew and felt at home in the neighborhood where McAuliffe had been reared, Biden said, “I knew him before I met him.” Alluding to McAuliffe’s flat, nasal upstate New York voice, Biden added, “It doesn’t matter what the accent is — it matters what the accent is on.”