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 key 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 reluctant to back the party in part because of its position on illegal immigration. With Mr. Romney having taken 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 Mr. Romney’s message on the economy but did not like his tough immigration talk.

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

Mr. Romney acknowledged his problem when he told donors in Florida recently that if President Obama keeps his commanding advantage among Latinos, it “spells doom for us.” He campaigned this week with Senator Marco Rubio of Florida, a Cuban-American, and signaled on 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.

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