In Monday's debate, Romney was asked how he would reduce the number of illegal immigrants in the United States if he is opposed to mass deportations. The former Massachusetts governor said programs like E-Verify could be used to eliminate the financial incentive to remain in the country.

"If people can't work here, they're going to self-deport to a place where they can get work," Romney said.

Asked by The Hill how Romney's comments could be construed to imply that illegal immigrants should be denied basic necessities, Medina pointed to Romney's close relationship with Kansas Secretary of State Kris Kobach, who has endorsed Romney. Kobach has been credit with writing most of Alabama's harsh anti-illegal immigration law, which has been challenged in the courts.

"Mr. Romney has said he wants to support and he joins in supporting Kris Kobach," Medina said. "When he says he supports those kinds of policies, he has to own all of it."

"This is a dishonest smear from President Obama's liberal allies and a desperate attempt to distract from his abysmal record," said Romney adviser Albert Martinez. "It will do nothing to help the millions of Hispanics who have been hit especially hard as a result of the Obama economy."

Martinez said Hispanics, like all Floridians, believe Romney is the best person to rebuild the economy and to replace Obama.

Romney has taken a more hard-line stance on immigration than most of his Republican rivals — most notably Newt Gingrich, who trounced Romney in South Carolina and who polls now show is leading Romney in Florida, a state with a large Hispanic population.

Florida will hold the next presidential primary on Jan. 31, and both Democrats and Romney's GOP competitors are hoping to use his strict stance on illegal immigration against him with Hispanic voters in the state.

Medina also accused Romney of hypocrisy for pandering to Hispanic voters in Spanish-language ads, then insulting them with his rhetoric in English and with endorsements from people like Kobach.

"Mitt Romney and other Republicans seem to forget Latinos speak English, too," Medina said. "We know what they say about us."

—This post was updated at 2:15 p.m. and 6:01 p.m.