KISSIMMEE, Fla. >> If Mitt Romney is to overcome his problem with Hispanic voters, he is going to have to start by changing a lot of minds in central Florida.

A crucial battleground in a vital swing state, the region is home to growing numbers of non-Cuban Hispanics who have always been viewed by Republicans as open to their economic and social views but deterred from backing the party in part because of its position on illegal immigration. With Romney having taken especially hawkish stances on immigration during the primary season, he and his campaign are now trying to shift the debate to what they feel will be friendlier terrain — jobs.

But the challenge here in central Florida is clear. Gladys Thayer, a native of Panama who is a registered Republican, is receptive to Romney’s message on the economy, but did not like his tough talk on immigration.

“I definitely think he needs to lean more towards helping the Hispanic community,” said Thayer, a real estate agent, who has not decided if she will vote for Romney in November.

Romney acknowledged his problem with voters like Thayer when he told donors in Florida recently that if President Barack Obama keeps his commanding advantage among Latinos, it “spells doom for us.” He campaigned this week with Sen. Marco Rubio of Florida, a Cuban-American, and signaled Monday that he may be open to compromise on the Dream Act, a path to citizenship for undocumented immigrants brought to the United States as children.

But whether Romney can make real inroads among Hispanic voters here and in swing states across the nation remains an open question. Though Cuban-Americans in south Florida favored the Republican candidate, John McCain, in 2008, Obama won 57 percent of Hispanic votes in the state thanks to Puerto Ricans and immigrants from Latin America.

“The question is, can the Republicans change that?” said Dario V. Moreno, a political scientist at Florida International University. “If they perform as they did four years ago, they will lose Florida.”

Much of the fight will be waged in and around Orlando, a region where population growth led to the creation of a new congressional district for 2012 in which Hispanics, many of Puerto Rican heritage, are 41 percent of the voting-age population. And while they have increasingly become part of the home-owning class, getting them to register to vote and turn out at the polls is a challenge both parties face.

The new district is centered in Kissimmee, the seat of Osceola County. Hispanics registered as Democrats outnumber Republicans by 35 percentage points, but many votes are considered up for grabs: Rubio, the Republican and Tea Party favorite, carried the district in 2010. It is no coincidence that the Republican National Committee’s director of Hispanic outreach for Florida, Pablo Pantoja, who was named last week, is based in nearby Orlando.

“Hispanics in the area are going to realize the Republican Party is where they belong,” said Pantoja, whose role will eventually be merged into the Romney campaign.

The wave of Puerto Rican migration here began in the 1970s; immigrants were attracted by good schools and houses sold to buyers still living in Puerto Rico, sometimes marketed with a trip to Disney World. The Republican economic message has had a natural resonance with some of these transplants. “I came to the United States during the Ronald Reagan years when I was 14,” said John Quinones, a lawyer, who is running as a Republican for Congress in the new 9th District. “I was very much influenced by his philosophy. If you work hard and play by the rules, you can get ahead in life.”

As Romney courts these voters, Rubio, a potential vice presidential choice, could help bolster his appeal in Florida and other swing states like Colorado and Nevada, and offer a counterweight to the harsh immigration rhetoric of the primaries. Last week, Rubio urged Romney and Republicans to compromise on the Dream Act to give undocumented students in college brought to the United States as children a legal residency status.

In the Republican debates, Romney had fiercely attacked a Texas Dream Act that allowed some undocumented students to pay in-state college tuition, calling it a “magnet,” and he alarmed Hispanic leaders with talk of “self-deportation,” which would induce illegal immigrants to leave voluntarily by making life more difficult through tougher enforcement measures.

Even as Romney now weighs moderating his immigration stances, his main approach is to appeal to Hispanic voters by pinning the blame for their economic woes on the failure of the president’s policies.

“President Obama Isn’t Working for Hispanics” was the headline of a campaign broadside last week. It cited figures showing the Hispanic unemployment rate is 2 points higher than the national average, and Hispanic households lost 66 percent of their net worth in the recession.

But the problem for Romney is that though Hispanics are suffering disproportionately, and like other voters they say jobs and the economy are their top concerns, polls show that they are not blaming Obama.

“When they say the economy is bad, yes, Latinos believe that, but they think it’s bad because of the Bush tax cuts,” said Matt Baretto, a political scientist at the University of Washington who surveys Hispanic voters.

Obama retained the support of 67 percent of registered Latino voters in a nationwide telephone poll released last week by the Pew Research Center, the same historically high figure he achieved in the 2008 election, according to the exit poll conducted by Edison Research.

Romney, who is well behind the president’s re-election campaign in grass-roots organizing, plans to bring on national Hispanic policy and media coordinators soon.

Jim Messina, Obama’s campaign manager, said he “felt sorry” for six new state directors of Hispanic outreach the Republican National Committee named last week in Florida and other battleground states.

“I think they’re having one person per state, whereas we’ve had operations on the ground over a year,” Messina said in a conference call. The campaign rebutted Republican claims of Hispanic hardship by asserting that 1.2 million new jobs have gone to Latinos under the president and 9 million Hispanics would acquire health insurance under his health care law.

Romney does have his backers here. On Saturday in Kissimmee, over a breakfast including rice and beans at the Taqueria Tres Amigos, Raymond Millan said he would vote for Romney over Obama.

“Even though both have good points, I have the tendency to lean toward the Republican,” said Millan, director of operations for a regional courier company. He said that when he was growing up in Puerto Rico, his family favored Republicans, and “I decided I should remain” faithful.

But support for Obama runs deep. Lissette Martinez said the president had kept his promises to withdraw troops from Iraq, expand health insurance, and, no less, helped save her home.

Martinez, who was getting a manicure-pedicure at a strip mall, said she and her husband, Jason, a county employee, were rescued by a government loan modification program that kept their house out of foreclosure.

Under a program created by the Obama administration, “they put us on a payment plan” pegged to their monthly income, she said, “and that’s really helped us.”

The loan modification program, subsidized by government payments to lenders, has had many troubles since its introduction in 2009, but Martinez expressed gratitude to the president.

“It’s going to take some time for him to undo what was previously done,” she said. “But he’s been doing everything he said he would do.”

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