If you remember the fight over the 2000 recount, Gore was demanding selective hand recounts in the four Florida counties he did best in. One of his best showings was in Miami-Dade, which is home to one of the biggest shares of Florida's Hispanic population. According to the 2000 census, 57.3% of the population in Miami-Dade is Hispanic or Latino origin, and Miami has one of the biggest concentrations of voters of Cuban ancestry in the country. Bush got around 46% of the vote in Miami-Dade (again, better than the “average” Republican... Romney got 38% against Obama in the same county in 2012) Still, the “Cuban vote” couldn't carry the ground zero location of the Elian Gonzales controversy for Bush, let alone the overall state or country as a whole.
The Cuban vote has been Republican. Only recently has it started to sour. Witness Obama winning FL-26 (which elected a rat over a scandal-plagued Republican) and FL-27 in 2012 whereas he lost them in 2008. He got over 60% in Miami-Dade, better than his showing in Palm Beach County!
Gore in 2000 got only 52.5% in Miami-Dade. I’m sure Bush won the Cuban vote that year also. Gore was trolling for Black votes in the recount.