Arguably the state's most popular Cuban-American politician, Sen. Marco Rubio, has withheld an endorsement during the primary but came to Romney's defense in the past week, criticizing Gingrich over an ad that labeled Romney anti-immigrant.
Gingrich, for his part, has called for a U.S.-supported "Cuban spring" uprising against the long-standing communist regime.
If elected, he told a crowd of Hispanic business and civic leaders Friday, he would bring to bear "the moral force of an American president who is serious about intending to free the people of Cuba, and willingness to intimidate those who are the oppressors and say to them, 'You will be held accountable.'"
Gingrich has talked of covert action to overthrow the government of Raul Castro, though he insisted such efforts would not include violence.
And he signed a pledge to roll back the ability of Cubans to visit and send money to relatives on the island to the strict limits Bush imposed in 2004. Such promises play well in the older exile community, many of whose homes were confiscated during the Cuban revolution and are far less likely than newer Cuban immigrants have close family there.
Gingrich also aired a Spanish-language radio ad in South Florida, reminding voters of Romney's 2007 presidential campaign gaffe, in which he proudly declared in Little Havana, "Patria or muerte, venceremos!" (Fatherland or death, we shall overcome) — not realizing the line was a slogan of Fidel Castro.
All that has helped sway retired insurance agent and Cuban exile Bernardo Diaz.
Last week, he declared his vote for Romney.
"I don't want Obama, and he's the only one who can win," Diaz said, as he puffed on a cigarette outside the famed Versailles Restaurant in Miami's Little Havana.
Days later, he had changed his mind, saying: "I'm leaning toward Gingrich. Gingrich seems more energetic, stronger on Cuba."