Perhaps the most politically-related story to hit headlines amid President Barack Obama’s recent inauguration weekend was Vice President Joe Biden hinting toward a potential run for president in 2016.

On Saturday, Biden attended the State Society of Iowa "First in the National Celebration," where he slipped up and referred to himself as the president instead of as the vice president.

"I'm proud to be president of the United States, but I am prouder to be …" Biden said, as the crowd started to laugh and cheer. "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."

While Biden quickly corrected himself, some have interpreted his slip-up to be something more. Rumors that Biden might be planning to run for president in 2016 have been swirling for a while, and early polls show he'd be a popular candidate.

Seemingly planting seeds for a run in four years, Biden invited members of two other early primary states — New Hampshire and South Carolina -- to attend his official swearing in at the Naval Observatory on Sunday. According to a pool report, as cited by ABC News, the vice president even had a seat reserved for South Carolina Democratic Party chair Dick Harpootlian.

On Monday, doing the honors for Biden’s swearing-in at the presidential inauguration ceremony was Supreme Court Justice Sonia Sotomayor, who was the third woman and the first Hispanic to ever issue the oath. Biden then made his way over to the Latino Inaugural Gala, where he commended the respective community for making its voice heard in the recent election.

“One thing that happened this election, you spoke, you spoke in a way that the world — and I mean the world as well as the United States — could not fail to hear,” Biden said.  “The fact that the Hispanic and Latino community in this country was such a decisive voice in turning out in this election was noticed by the whole hemisphere … I think you underestimate your power. I think you underestimate what you’ve done for America and what you’re about to do.”

If Biden were to run in 2016, polls cited by CNN show he'd be a popular candidate, though not as popular as Secretary of State Hillary Clinton, who's also believed to be considering a run.

A CNN/ORC Poll taken Dec. 17-18 showed 66 percent of Democrats would support Biden in a presidential bid, compared to 85 percent who said they would support Clinton.

Meanwhile, a more recent CNN recent poll, released this week, showed the vice president's approval rating at 59 percent, with 38 percent saying they disapprove of the job he is doing. Biden's approval rating is up five points from last month.