Vice President Joe Biden has barely hidden his possible interest in running for president in 2016, and now, the loquacious former senator has begun to lay the groundwork for a potential campaign to succeed President Barack Obama.

"In a couple years, I think he's going to take a hard look at it," Beau Biden, the vice president's son and the attorney general of Delaware, said on MSNBC. "I hope he does."

A potential Biden bid for the presidency will come as little surprise to observers of the vice president over the past few years; Biden has often dropped hints of his interest in running as Democrats' nominee in 2016, and has repeatedly refused to rule out running in 2016 when asked.

Biden further stoked speculation this inaugural weekend, when he stopped by the Iowa State Society's inaugural ball, and invited top New Hampshire Democrats to his formal swearing-in ceremony on Sunday. Both Iowa and New Hampshire traditionally host the first two nominating contests of a presidential cycle.

At the Iowa ball, he mistakenly referred to himself as president, before correcting himself. “I’m proud to be president of the United States,” he said before pausing to rephrase. “I’m proud to be vice president of the United States but I am prouder to be Barack Obama, President Barack Obama’s vice president.”

And on Monday, during the inaugural parade, he glad-handed his way down Pennsylvania Avenue. Biden waved and pointed at parade-goers on the sidelines, and even ran over to shake the hand of NBC’s Al Roker, positioned behind a security barricade.

When he ran into a Republican voter in Florida during the closing days of the campaign, Biden cautioned the Obama administration's health reform law would be a chit in his column during the next presidential campaign. "After it's all over when your insurance rates go down, then you'll vote for me in 2016," he said, employing a quip that quickly drew attention for its electoral implications.

Biden has twice run for president before, in 1988 and 2008. And each time, his candidacy flamed out. In the '88 campaign, Biden withdrew before the first nominating contest following allegations that he had plagiarized portions of speeches.

Biden survived through the Iowa caucus in 2008, but ended his campaign following a fifth place finish in the contest. The then-Delaware senator committed some trademark gaffes during that campaign, too. Biden joked, for instance, about how "you cannot go to a 7-Eleven or a Dunkin' Donuts unless you have a slight Indian accent." He also memorably referred to Obama, his future boss, as "the first mainstream African-American who is articulate and bright and clean."

But Biden, who served in the Senate from 1973 to 2009 and established himself as an expert on matters of foreign policy, now finds himself arguably at the apex of his political strength. Forty-one percent of Americans said they have a positive impression of the vice president in the most recent NBC News-Wall Street Journal poll, versus 37 percent who have a negative impression of Biden. Those aren't blockbuster numbers, but they're among Biden's best in the history of the poll.

But a successful run in 2016 would make Biden the nation’s oldest inaugurated president.  He turns 74 in 2016, a year older than Ronald Reagan when he took the oath at his second inaugural.

Biden emerged during the 2012 Obama campaign as a key asset of the president's, stumping repeatedly in key blue collar corners of swing states like Ohio and Wisconsin. During those stops, the vice president offered some of the sharpest criticism of Republican nominee Mitt Romney's policies in a direct appeal to middle class voters.

Brian Snyder / Reuters

Vice President Joe Biden and his wife, Dr. Jill Biden, dance at the Commander-in-Chief's Ball in Washington, Jan. 21, 2013.

Biden acted as a key player during the president's first term on matters ranging from foreign policy to domestic. Biden was tasked with implementing the 2009 economic stimulus, and Obama asked him more recently to lead the task force that developed recommendations to curb instances of gun violence.

Obama has also repeatedly turned to Biden to lean on his long-standing relationships in the Senate to help forge deals with Republicans. When talks to avert the "fiscal cliff" reached an impasse late this past December, Senate Minority Leader Mitch McConnell, R-Ky., reached out to Biden, who won some of the credit for the last-minute deal.

Still, Biden has also become a favorite target of conservatives during the last four years, not least of which because of his not-infrequent gaffes. Conservative media outlets enjoyed stoking speculation, for instance, that Obama might bump Biden off of the ticket in favor of Secretary of State Hillary Rodham Clinton -- suggesting that Biden had become too big of a liability to the president's re-election campaign.

And indeed, there were moments during the 2012 campaign where Biden veered badly off script. When he expressed his personal support for same-sex marriage during a May 6 appearance on NBC's "Meet the Press," he preempted Obama's own anticipated endorsement of gay and lesbian marriage rights. Obama was forced to hastily follow in the footsteps of his vice president.

Biden also won the enmity of the Romney campaign when he told a predominantly African-American audience that the GOP ticket's economic policies would "put y'all back in chains."

But despite Biden's propensity to fall off-message on occasion, he still enjoys a champion in one key ally: Obama.

"One decision I know was absolutely correct -- absolutely spot on -- was my choice of vice president," Obama said Sunday at an inaugural reception. "I could not have a better partner than Joe Biden."

That's a line that Biden would no doubt love to feature in a campaign ad in just a few years. He might not be the only Democrat in the race -- many in the party hope that Clinton will seek the nomination again -- though the vice president's door to running is open than ever.