WASHINGTON -- A few days into President Barack Obama's second term, talk has already turned to who will run to succeed him in 2016 -- and his often unscripted vice-president has become the latest favourite in the guessing game.

Social media loves to describe Joe Biden as a kind of off-colour but loveable uncle, and the satirical website The Onion has buffed his bumbling, every-guy image with its fake stories about him washing his favourite sports car, shirtless, in the White House driveway or sucking down tall beers.

But Biden has also been called perhaps the most influential vice-president in U.S. history, and his decades of experience in the Senate have been used to help broker deals on the recent so-called "fiscal cliff" and lead on issues such as gun control.

Biden can be famously off-script, but even that has ended up pushing for change. His comment during an interview last year that he was "absolutely comfortable" with gay marriage led Obama to come out in support of it himself, earlier than his staff said he had planned.

The vice-president, who practically danced his way along the parade route after Obama's inaugural ceremony on Monday, is dropping plenty of hints that he may try to cement Obama's legacy with his own presidential campaign in 2016.

Outgoing Secretary of State Hillary Rodham Clinton remains the heavy favourite of the Democratic party faithful, many of whom would like to see her as the first female president, but Biden is making clear that he has no intention of closing any doors that could lead to the White House -- especially if Clinton decides not to run.

As vice-president, Biden can stay in the spotlight, and he is no stranger to the rigours of a presidential campaign after two unsuccessful bids in 1988 and 2008.

"There's a whole lot of reasons why I wouldn't run," Biden, who will be nearly 74 on Election Day in 2016, told CNN before the inauguration. "I don't have to make that decision for a while. In the meantime, there's one thing I know I have to do, no matter what I do. I have to help this president move this country to the next stage."

White House press secretary Jay Carney on Wednesday reiterated Biden's focus on helping the administration achieve Obama's goals, which Carney said was demonstrated most recently in the effort to deliver to Obama a package of policy proposals to reduce gun violence.

"That's the vice-president's focus, in his own words," Carney said. "It was when I worked for him, it was throughout the first term, it is now. As he said, other considerations are for the future. He's focused on his work as vice-president as the president's partner."

Yet Biden is doing nothing to tamp down the speculation.

Biden's private swearing-in ceremony Sunday was attended by recently elected New Hampshire Gov. Maggie Hassan, someone who would be a potent ally in the state's first-in-the-nation primary in the long election process. Attendees at a Sunday reception at the vice-president's residence said they noticed a lot of party activists from early voting states like New Hampshire, Iowa and South Carolina.

During the weekend, Biden attended several inaugural balls with Democrats who would energize a presidential campaign. At the Iowa State Society Inaugural Ball, Biden told partygoers he was "proud to be president of the United States," prompting cheers. He quickly corrected himself, saying he was "proud to be vice-president of the United States, but I am prouder to be ... President Barack Obama's vice-president." Laughing it off, he said, "There's goes that."

At a ball celebrating Latino voters, Biden said the Hispanic community was "a decisive factor" in the 2012 election. "This is your moment," Biden said. "America owes you." Some party stalwarts said it was noteworthy that Biden asked Supreme Court Justice Sonia Sotomayor, the first Latina justice, to administer the oath of office.

"It seems obvious that he's going to keep that option open for himself and do the right things," said Mike Gronstal, the Democratic leader of the Iowa state Senate, who attended the Naval Observatory reception. Gronstal said Biden actively worked the room, thanking supporters for their help during the 2012 campaign.

If Clinton decides not to run, Biden could draw upon good will from Obama's voting coalition, an ability to connect with regular folks and extensive campaigning in key states like Iowa, New Hampshire, Florida and Ohio. But he would also need to deal with personal poll numbers that rank below Obama's and a propensity to say unscripted things in an era where political gaffes can quickly sink a campaign.

New Hampshire state Sen. Martha Fuller Clark, who was among the attendees at Biden's Sunday reception, said it was "early to read into" Biden's interest in 2016 but said there was "huge support" in the key primary state.

"He's deeply admired and loved in New Hampshire," Clark said. "Clearly, Joe Biden occupies a key place in our hearts."