They may enjoy the food, but Republicans could get indigestion from recent polls showing President Barack Obama set to win more than 60 percent of the Hispanic vote nationwide.
But the Hispanic vote is not monolithic. Hispanics here in the east coast state of Florida, for example, often hold different political opinions from those in the Southwest.
And there is diversity even among Tampa's Hispanics.
“I am not voting for Obama because he has not done anything these four years," said Cuban-American barber Jose Mario Farina, who says he favors Romney. "He has not made a change and he hasn't done anything.”
But Elena Alfonso, an immigrant from Colombia, likes Obama.
“I like how he has represented the country and he gave opportunity to the immigrant students, a good accomplishment.”
Prominent Hispanic Republicans like Florida Senator Marco Rubio and New Mexico Governor Susana Martinez made a pitch to Hispanic voters at an event here Monday.
Also on hand was Mitt Romney's Spanish-speaking son, Craig. He said Hispanics will support his father once they get to know him.
These delegates are from the southwestern state of Arizona, where tough Republican-led measures to slow illegal immigration have offended many Hispanics.
But Arizona delegate Jose Borrajero, an immigrant from Cuba, says he and others like him think many Hispanics should identify with conservative social values championed by Republicans.
“Our main objective is to preach this gospel, in other words to tell Hispanics that 'Hey, you do not have to be a liberal Democrat, if your last name ends in a vowel or a z, you do not have to be a liberal Democrat,” he said.
That may be a tough sell, though, and some Republican strategists worry that failure to attract more Hispanics this year could hurt the party's prospects in future elections, when Hispanics will comprise an even larger part of the voting population.