The survey, conducted by Democratic firm Public Policy Polling, gives Rubio narrow leads over two potential Democratic opponents, Rep. Debbie Wasserman Schultz and former gubernatorial nominee Alex Sink.

Rubio has 45 percent support to Sink's 42 percent support, and 46 percent to Wasserman Schultz's 43 percent support among Florida voters.

But he fares much better than West, who previously indicated he'd run for the seat if Rubio chooses instead to run for president. Sink leads West with 44 percent support to his 38 percent and Wasserman Schultz takes a four-point lead, 44 to 40 percent support.

The survey was conducted among 579 Florida voters from Sept. 27-29 and has a margin of error of plus or minus 4.1 percentage points.