A new poll from Quinnipiac University released Thursday reveals that President Barack Obama, who carried Florida in 2008, faces a tough time carrying the Sunshine State in 2012, while Democratic incumbent U.S. Sen. Bill Nelson remains in solid shape for his battle to win a third term.

The poll found that a majority of those surveyed -- 52 percent -- disapprove of Obama’s performance in office, while 44 percent approve it. This compares to a Quinnipiac poll released on Feb. 3 in which the president’s approval stood at 47 percent and the disapproval was at 49 percent. In the new poll, more Republicans -- 84 percent -- disapprove of Obama’s presidency than Democrats in the state -- 79 percent -- who approve it. The poll finds that a majority of independent voters -- 55 percent -- disapprove of Obama’s performance, while only 39 percent approve of it.

While Obama’s disapproval numbers are on the rise, the poll finds that he will still be competitive in the 2012 general election in Florida. A majority of those surveyed -- 51 percent -- thinks the president does not deserve a second term as opposed to 42 percent who think he does, but a generic Republican challenger is ahead of the president by only 3 points in the poll, 41 percent to 38 percent. This compares to the February poll in which the unnamed Republican candidate took 42 percent with Obama behind at 40 percent.

“With President Barack Obama formally announcing his re-election campaign this week, one can expect that his team will be focusing on Florida, one of the nation’s pre-eminent swing states and one that the president carried in 2008,” said Peter Brown, assistant director of the Quinnipiac University Polling Institute.  “He has some work to do in the Sunshine State. On job approval, re-election and the matchup against an unnamed Republican, he does a good deal better among women than he does among men.”

But the poll also finds that, while most Floridians do not like his policies in office, they like Obama. The poll found that 40 percent like him and his policies; 30 percent like him but not his policies; 24 percent do not like him or his policies; while 1 percent dislike Obama but back his policies.

“Despite questions about his policies, the president is personally popular with Floridians,” noted Brown.