MIAMI (CBSMiami/AP) – While the campaigns of both President Barack Obama and Mitt Romney try to come up with ways to court the Hispanic vote, they’re learning that there is no one size fits all approach to the nation’s fastest-growing minority group.

In Miami, Colombia native Luna Lopez probably will vote for President Obama now that he’s decided to halt the deportation of many illegal immigrants brought to the United States as children.

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In Arizona, Mexican immigrant Carlos Gomez backs Republican Mitt Romney because he’s more conservative on social issues than his Democratic opponent.

In New Mexico, Tomasita Maestas says she will pick the presidential candidate who has the best plan to fix education and the economy.

Immigration policy would seem to be the natural top issue for these voters, except that nearly two-thirds of Hispanics are born in the U.S. Their priorities are the same as the general population — jobs, the economy, education and health care.

“We need to see more jobs here, that’s my No. 1 priority and what I want to hear about,” says Stefan Gonzalez, an almost 18-year-old from Denver. Gonzalez, who works in a suburban Denver pawn shop, says he plans to vote for Obama this fall.

In Albuquerque, Ernest Gurule, an 84-year-old whose ancestors settled New Mexico in 1580, says his main issue is the federal health care plan upheld by the Supreme Court last week, and that he’ll back Obama in part because of it. Also, the Democrat, adds: “It’s too expensive to change horses midstream.”

In the short term, these voters could decide the outcome in Florida, Nevada, Colorado, New Mexico and elsewhere. The long-term stakes are even bigger because Hispanics are projected to account for roughly 30 percent of the population by 2050, doubling in size and, potentially changing the national political landscape.

Like most minorities, Hispanics traditionally have leaned Democratic. But a recent Pew Research poll indicates that Hispanics also are the fastest-growing group of independent voters, with 46 percent now shunning a party label compared with 31 percent six years ago. Such results only underscore how diverse Hispanics are and the challenges for the political parties.

“It is going to be a very hard fight to win,” says Jennifer Korn, the executive director of the Republican-based Hispanic Leadership Network, which was established to help bring more Hispanic voters to the GOP. “The more they assimilate, the more sophisticated they become and that’s when they start dividing between parties.”

For now at least, Obama and his Democrats have an advantage, with the latest polls showing 65 percent of Hispanics back Obama and 25 percent back Romney.

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The Democrats’ campaign has worked to keep that edge, helped by Obama’s new immigration policy and the Supreme Court’s decision to side with the administration on most of an Arizona law that many immigrants viewed as overly harsh.

His campaign has spent the past year setting up offices with grassroots outreach to Hispanic communities in the Southwest, as well as in important states such as Ohio, North Carolina, Pennsylvania and Florida.

Mindful of the diversity among Hispanics, Obama has custom-tailored his outreach, including tweaking Spanish dialect for different regions.

For instance, in Florida the campaign has two distinct outreach plans. One focuses on Cuban-Americans in Miami who tend to lean Republican and are less concerned about immigration; the other speaks to traditionally Democratic Puerto Ricans, who are U.S. citizens from birth, as well as new immigrants from Central America.

Obama also has promoted the new health law, which can resonate in states such as New Mexico, which has one of the highest rates of uninsured in the country.

Romney has plenty of ground to make up after a bruising primary season filled with tough rhetoric that even Republicans acknowledge turned off many Hispanics. He recently established a Hispanic advisory group that includes top elected Republican Hispanics.

During the primaries, the former Massachusetts governor pledged to veto legislation, known as the DREAM Act, that would give a path to citizenship to young immigrants who came to the United States illegally as children but have since attended school or served in the military. He has since toned down his anti-immigration stance, which included self-deportation, telling a Hispanic leadership gathering in Miami that he would address illegal immigration “in a civil but resolute manner.”

Alexandra Franceschi, a spokeswoman for the Republican National Committee’s Hispanic effort, made clear that the GOP outreach will focus broadly on the economy.

“Hispanics are Americans and are facing the same issues as everyone else, chronically high unemployment, lower pay and rising health care costs,” she said.

Republicans have noted that under Obama, the Hispanic unemployment rate is higher than the national average. And Hispanics’ median household income fell 7 percent between 2000 and 2010, from $43,100 to $40,000, according to the Pew Hispanic Center.

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