On the phone at a campaign stop in Sarasota last week, Joe Biden pressed his argument to the Republican brother of a supporter, defending Obamacare to the skeptical man.

“And after it’s all over, when your insurance rates go down, then you’ll vote for me in 2016,” Biden said in earshot of reporters capturing his every word.

The vice president made the comment in a joking manner. But the mere mention of 2016 again raised questions: Is Joe going to give it another go?

This election is President Obama’s last. But the end of one campaign always marks the beginning of another, and Biden, who has twice run for the top job, could be a central figure in the next presidential election.

The vice president has been unclear about whether this is his final campaign. Soon after Biden voted near his Delaware home Tuesday morning, a reporter asked whether this day would mark the last time he would cast a ballot for himself. Biden grinned and responded, “No, I don’t think so.”

Later the same day, as Biden shook hands and took photos with voters at an Ohio restaurant, a woman wanted to know, “After Obama wins this election are you going to run?”

Biden said, “Oh, I’m going to go back home and run for county council or something.”

All joking aside, Biden’s friends and advisers say he has been squarely focused on winning another four years for the Obama-Biden ticket. Any decisions about a future run are likely to be made in the coming months after a meeting of Biden’s inner circle, said Ted Kaufman, a close friend who served as Biden’s chief of staff for 19 years and succeeded Biden in the Senate.

“We’re just glad this campaign is ending,” said another Biden senior adviser this week. “That’s a topic for another day.”

The vice president, who in recent days has seemed to relish teasing about his political intentions, did more than 130 events for the ticket.

In the past four years, he has been a major player in the Obama White House, carving out a role that onlookers liken to an assistant president. He was the administration’s point person on winding down the war in Iraq, a leading figure in White House negotiations with Congress on deficit reduction and largely responsible for implementing the stimulus, personally calling local officials to cut through red tape.

But his “honest Joe” persona has created a dueling narrative of verbal gaffes and slip-ups. He took some ribbing for publicly declaring his support for same-sex marriage this summer, stepping on Obama’s plan to make his own announcement.

Behind campaign podiums, Biden’s off-the-cuff remarks were sometimes a distraction in the 2012 race, feeding “that view of him as not a serious person,” said Jules Witcover, a journalist and author of “Joe Biden: A Life of Trial and Redemption.” At a campaign stop in Virginia, for example, Biden warned a racially diverse crowd that his opponent’s approach to regulating the financial industry will “put y’all back in chains.” During his debate with GOP vice presidential contender Paul Ryan, Biden laughed often and rebutted Ryan’s statements on Libya as “a bunch of malarkey.”

What resonated with much of the Democratic base was Biden’s populist rhetoric and aggressiveness on display throughout the campaign and especially during the debate, said former Congressman Tom Perriello, president of the liberal Center for American Progress Action Fund.

“This is an election that ended up being very much about manufacturing and the middle class,” Perriello said. “Few people are able to deliver that clear message on what it means for the middle class to have a fair shot better than Joe Biden.”

While Biden drew crowds of supporters — usually a few thousand — who asked him whether he would run in 2016, there were also those who suggested that Biden’s time has passed. Should he run, Biden would be 74 on inauguration day in January 2017, one of the oldest Americans to seek the country’s highest office.

On the campaign trail these past 18 months, Biden put on an energetic face, bounding up and down the stairs of Air Force Two wearing his standard uniform of blue blazer and black aviator sunglasses.

With Obama’s victory Tuesday, Biden will have another four years to shore up his image and plot his own future. Whether he stands for election in 2016 will be a family decision.

In the final weeks of the Obama-Biden campaign his sister Valerie Biden Owens, who is the vice president’s best friend and closest adviser, has been regularly at his side. She managed each of his campaigns. In fact, the entire Biden clan dove into this campaign. Jill Biden, the vice president’s wife, maintained a robust schedule on the trail after the Democratic National Convention, speaking at community colleges and campaign offices around the country. Biden’s son Beau, who is attorney general for Delaware, also stumped for the ticket.

Biden’s first run for office ended disastrously in the summer of 1987 when his campaign disintegrated amid allegations that he had plagiarized speeches. He returned to the Senate, where he served six terms. In 2008, the Biden family practically moved to Iowa, but Biden’s campaign never got traction.

“He ran into the buzz saw of Hillary and Obama,” Witcover said. “He really had no chance.”

If he runs again, Biden will have to maneuver through the awkward political dance that burdens vice presidents seeking the presidency. They must form their own political identity without seeming disloyal to the president they serve.

Unless Biden rules out a third attempt, he’ll be considered a key challenger in what could be a crowded 2016 field, said William A. Galston, an aide to President Clinton who is now a senior fellow at the Brookings Institution.

“The late [congressman] Morris Udall said the only cure for wanting to be president is embalming fluid,” Galston said.