Rubio has announced that he will make his own decision about whether to jump into the race and won't defer to Bush or anyone else. He also has said that if he does enter the contest, he won't seek re-election to the Senate, which would open his seat to intense competition among Republican and Democratic contenders.

The results could shake up the state's political scene, analysts say, by dividing Republican loyalties between Rubio and Bush and removing a popular incumbent from the Senate race in 2016.

"It certainly would put the Senate seat in play, and it certainly would be a competitive race," said Richard Conley, a political scientist at the University of Florida who tracks presidential politics.

"Florida is a swing state and unpredictable. Frankly, if you look at the last presidential election, Republicans have reason to be worried."