Just this week he jokingly told a voter in Florida that he should vote for Biden in four years after the man's health insurance rates drop because of Obamacare.
Biden's presidential aspirations are anything but a joke.
He ran for president in 1988 and again in 2008. If he ran for the White House in 2016, Biden would be 73, one of the oldest candidates for president in history, older by a few months than Ronald Reagan when he ran for re-election in 1984.
Biden aides say he will not make a decision until well after the election, when he sits down with family members and advisers for a heartfelt strategy session. It's the same process Biden used when he decided to run for president in 2008 - and when he passed up a bid four years earlier.
For now, Biden and his aides say he is focused exclusively on helping re-elect President Barack Obama. Biden maintains an active campaign schedule that has taken him to more than 120 campaign events this year, including eight states in the past two weeks.
Biden is so consumed by the election that he has little time - or inclination - to think about what comes next, said Ted Kaufman, a close Biden friend and former chief of staff who succeeded Biden in the Senate and has been involved in all of Biden's campaigns since 1972.
"In real life, you totally concentrate on one election at a time," Kaufman said.
Still, retirement is unlikely, Kaufman and other friends say. Biden is energized by the political game and shows no inclination to slow down. Biden frequently says a person is on the way up or the way down - and he does not want to head down.
While many former political luminaries such as Sens. Bob Dole, George Mitchell and others earned huge paydays at high-powered law firms, Biden is unlikely to follow suit.
As a former vice president, Biden could make big money on the speaking circuit or by writing a book - options he may pursue - but friends says he is not motivated by money. Biden and his wife, Jill, an English professor at Northern Virginia Community College, are financially secure, and Biden's three children are grown. Joe and Jill Biden reported adjusted gross income of $379,035 last year.
So what does a 70-year-old ex-vice president do?
Biden "could do anything," says former Ohio Gov. Ted Strickland, a close friend.
Biden could join a think tank or start his own initiative, focusing on foreign policy or family justice or labor, Strickland said.
"He's a person with considerable energy and a strong motivation to serve," Strickland said, noting Biden's Roman Catholic faith.
Strickland scoffs at the notion that Biden would cash in on his four-decade tenure in Washington, which includes four years as vice president and six terms in the U.S. Senate, where he chaired both the Judiciary and Foreign Relations committees.
"Anybody who knows Joe Biden knows he's motivated by a sense of responsibility that is almost religious in nature," said Strickland, who has traveled all over Ohio with Biden this year.
Biden, who commuted by train from Wilmington, Del., as a senator, likely would return to his home there, but probably would maintain a residence in Washington, where three of his five grandchildren live. The other two live in Delaware.
If he runs in four years, Biden has some obvious strengths.
He grew up in Scranton, Pa., and is seen as a champion of white, working- and middle-class voters. He also has strong support from unions and ethnic minorities as well as people in the gay community, who were encouraged by his early support of gay marriage.
Biden has been a regular presence in Ohio, a critical state on the electoral map, and has traveled often to Florida, Iowa and New Hampshire - key, early voting states for a possible 2016 run.
Biden has been "very successful at raising the enthusiasm level with our base," former Pennsylvania Gov. Ed Rendell said.
Even with those strengths, Biden's tendency to go off script - in Virginia he called Senate candidate Tim Kaine "Tom Kaine" - causes nervousness among the Obama campaign hierarchy. Transcripts of his remarks are not distributed to the press corps, in contrast to those of the president and first lady Michelle Obama.
Biden knows his fate is tied to Obama.
At an appearance at a campaign office in Iowa this week, he thanked volunteers and reminded them that Iowa was the state that put Obama "on the road" to the presidency in 2008.
"I may have been a little disappointed at the time," Biden said, "but we got the right order."
A supporter shouted, "You're our man in 2016!"
Biden glanced at the woman, but remained uncharacteristically silent.
(Copyright 2012 by The Associated Press. All Rights Reserved.)