Can Romney or Gingrich win over Latinos? In a Republican presidential primary that's included discussion of an electric border fence, it may not be surprising that a new poll shows Hispanic voters are skeptical of the Republican party. But as the GOP field narrows down (Herman Cain, who proposed the electric fence, is among the candidates who have dropped out of the race) and the race progresses to states with larger Latino populations, the candidates are stepping up their overtures to the critical voting bloc. Latino voters get their first real opportunity to weigh in on the GOP contest in the Florida primary on Tuesday. A new poll of Hispanic voters shows that of the remaining Republican candidates, Mitt Romney may be making the most inroads with the Latino community. The former Massachusetts governor garners 49 percent support among likely Republican Florida primary voters who are Latino, according to the Latino Decisions poll released Wednesday for Univision News and ABC News. That gives him a 26-point lead over his next-closest rival, Newt Gingrich, who wins 23 percent support. In Florida, about one in 10 Republican voters are Latino. Both in the state and nationally, Latinos are growing in number and political clout. Latino voter turnout in Florida grew a 81 percent from 2000 to 2008, according to the Census, and nationally, turnout grew by 64 percent in that time frame. About 10 million Latinos voted in 2010, and some expect about 12 million to vote in November. Yet even as Latinos become a clear political force, the Republican party has had trouble balancing its overtures to the community with its engagement with the Tea Party and other conservative voters looking for more stringent immigration solutions. Romney wishes Castro gone Gingrich pulls Spanish-language ad after complaint from Rubio Newt Gingrich takes a risk, aims for broad appeal For instance, in a Florida debate Monday, Romney softened his language on the Dream Act, saying he supports some elements of the bill, which would give a pathway to citizenship to some undocumented young people. At the same time, he left some Latinos bristling with his suggestion that he would reduce the number of undocumented immigrants in the U.S. with "self-deportation." That may be why just 17 percent of Latinos, according to the Latino Decisions poll, say Republicans are doing a good job reaching out to Hispanics. As many as 45 percent say the GOP doesn't care about them, and another 27 percent say the party is downright hostile to Hispanics. Romney's "beginning to understand he's in a deep hole with the Latino community, but he can't seem to stop digging," Eliseo Medina, the secretary-treasurer of the Service Employees International Union (SEIU), told reporters this week. Romney's call for "self-deportation," Medina said, "really said to me what these candidates think about the Latino community -- basically, make their life miserable so that they leave the country." Gingrich, Romney in dead heat in new Florida poll GOP rolls out strategy to woo Hispanic voters Romney told Univision's Jorge Ramos on Wednesday that "immigration has been an extraordinary source of strength in this country," but that illegal immigration has to stop to spur more legal immigration. Focusing on the economic aspect of immigration -- and the economy overall -- is how the GOP will win Hispanic votes, Republicans say. "What's on [Latino's] minds is what's on your mind and my mind and everybody else's mind: How am I going to provide for my family?," Sen. Marco Rubio, R-Fla., said on CBS This Morning on Thursday. What I encourage our candidates to do is speak to that, and particularly as they are doing, I think, embrace the free enterprise system... I think that's where we win, I think that's where we're different than President Obama and his party. The Latino Decisions poll, as well as a poll released Thursday by Resurgent Republic and the Hispanic Leadership Network (GOP-aligned groups), confirm that the economy is still the top issue for Latino Floridians. The Hispanic Leadership Network poll also shows that there's room for Republicans to appeal to Latinos on issues like education reform, the national debt and even on the issue of state voter ID laws. Gingrich and Romney will address a conference in Florida on Friday hosted by the Hispanic Leadership Network, a center-right advocacy group, and could hit on those issues. Still, the issue of immigration hits close to home for Latinos -- a Latino Decisions poll from July 2011 shows that a majority of Hispanic Americans know an undocumented immigrant. An overwhelming majority have close relationships with immigrants, undocumented or otherwise. "Somewhere near 90 percent of all Latino citizens are within two generations of the immigration experience," said Gary Segura, a Stanford professor and co-founder of Latino Decisions. When you're speaking to Latinos about immigration, he said, "You are speaking about them, their parents or their grandparents." Gingrich, who has made more concerted efforts to reach out to Hispanics, told Univision's Jorge Ramos on Wednesday that Romney's "self-deportation" solution amounted to "an Obama-level fantasy." When Romney spoke to Ramos, he pointed out that Gingrich has also expressed support for "self-deportation" and accused Gingrich of pandering to the Univision audience. Latino activists and their allies who are opposed to the Republican candidates are charging that all of them -- Romney included -- are pandering. The SEIU teamed up with the pro-Obama super PAC Priorities USA Action to purchase a six-figure, Spanish-language ad buy in Tampa and Orlando blasting Romney as two-faced. Called "Las dos caras de Mitt Romney" (The two faces of Mitt Romney), the radio ad says in Spanish, "Mitt Romney has no shame. He shows one face to the Hispanic community and another completely different one to everyone else. Though he faces tough pushback from Latino activists working with Democratic allies like the SEIU, Romney has secured several endorsements from Latino Republican officials in Florida. His campaign released an ad on January 11 featuring Florida Reps. Ileana Ros-Lehtinen and Mario Diaz Balart, as well as former Rep. Lincoln Diaz-Balart. The ad is narrated in Spanish by Romney's son Craig. The latest Latino Decisions poll does show President Obama trouncing his potential competitors among Latinos nationally -- he beats Romney 67 percent to 25 percent in a head-to-head match up, and he beats Gingrich 70 percent to 22 percent. Still, the margin is smaller among Latinos in the key swing state of Florida -- there, Mr. Obama beats Romney 50 percent to 40 percent. Mr. Obama beats Gingrich 52 percent to 38 percent. Cubans, who vote more Republican than other Latinos, make up a large share of the Latino population in Florida. In the Resurgent Republic poll, Mr. Obama leads an unnamed Republican opponent by just 46 to 39 percent -- that's 11 points behind the 57 percent support he won among Florida Hispanics in the 2008 race. Resurgent Republic Board Member Whit Ayres said Florida Hispanics "think he's a weaker leader than expected, they think he has not fulfilled his promises."