“I have no intention of doing that. That doesn't make sense to me to even think about it, let alone plan to do that," Paul said Sunday on Fox News.

Bloomberg, who has not signaled any desire to run, also polls in the double digits against Romney and Obama, earning 13 percent of support. Obama again would receive 44 percent of the vote, while Romney would earn 35.

While the poll offered an intriguing picture into how a third-party bid could affect the presidential race, it also offered a few hopeful signs for Obama. 

Fewer respondents thought the country was headed down the wrong track than in October, the low point for his presidency. More respondents approve of how the president is handling the economy, more have a positive view of the Democratic Party and more say they would probably vote for Obama over a generic Republican candidate.

Obama also leads Romney in a head-to-head match-up by a 49-43 percent margin, up from only a two-point difference in October. Obama led Herman Cain by a 53-38 percent margin.

Respondents were also most likely to blame Republicans in Congress for the problems facing America.

But the president will still face a difficult road to reelection. Seventy-three percent of Americans still believe that the country is headed in the wrong direction, and just more than half disapprove of the job the president is doing.