As Republican leaders try to woo Latino voters with a new openness to legal status for the nation's illegal immigrants, the party remains at odds with America's fastest-growing ethnic community on another key issue: healthcare.

Latinos, who have the lowest rates of health coverage in the country, are among the strongest backers of President Obama's healthcare law. In a recent national poll, supporters outnumbered detractors by more than 2 to 1. Latinos also overwhelmingly see guaranteeing healthcare as a core government responsibility, surveys show.

Yet congressional Republicans continue to make repeal of the 2010 Affordable Care Act a top agenda item and have renewed calls for deep cuts in health programs such as Medicaid, which are very popular with Latinos.

"Obamacare is a colossal mistake for our country," Senate Minority Leader Mitch McConnell (R-Ky.) said recently in a speech on the Senate floor. "It needs to be pulled out by its roots."

Republican National Committee spokeswoman Alexandra Franceschi expressed confidence that Latinos would ultimately recognize that the law raises costs and burdens businesses. "We're going to do a better job explaining why this law is negatively affecting all Americans, including the Hispanic community," she said.

At the same time, however, attacking the law risks undermining the RNC's planned minority outreach campaign, which party leaders said in a recent strategy blueprint must convince Latinos "we care about them."

"This is going to hurt Republicans," said Matt Barreto, cofounder of Latino Decisions, a nonpartisan national polling firm. "When Republicans keep saying they will repeal the health law, Latinos hear the party is going to take away their healthcare."

Republican presidential nominee Mitt Romney received just 27% of the Latino vote in November, in large measure because of his harsh rhetoric about illegal immigrants. But he also made overturning the health law a central plank of his campaign. His first Spanish-language ad after he won the 2012 nomination promised he would issue an executive order to roll back the law on his first day in office.

Obama, meanwhile, made upholding the Affordable Care Act a core part of his Latino strategy. A quarter of the president's advertising in Spanish focused on the law, said James Aldrete, who oversaw Spanish-language media strategy for Obama in 2008 and 2012. "We knew from the start that, if Latinos knew about the benefits of the law, they were going back the president," he said. "It was central to our messaging."

In one widely aired television ad, Cristina Saralegui, a popular talk-show host, explained in Spanish how the law would help millions of Latinos get health insurance. In another, a campaign volunteer visiting a middle-aged man with diabetes, which is widespread among Latinos, said: "Family is important to President Obama, and he understands that families that are fighters sometimes have lost everything when someone gets sick."

Surveys indicate that close to 30% of Latino citizens and legal permanent residents lack health insurance. By comparison, just 11% of white and 17% of black Americans are uninsured, according to the latest data from the federal Centers for Disease Control and Prevention.

Starting next year, the health law will provide hundreds of millions of dollars in subsidies to low-income Americans and legal residents to help pay insurance premiums. Illegal immigrants cannot receive these subsidies.

The law will also provide states with additional federal aid if they open their Medicaid programs to more of their poor residents. That, too, will likely disproportionately benefit Latinos, nearly 30% of whom rely on government health insurance, at twice the rate of white Americans.

The high numbers of Latinos who are uninsured or depend on public programs reflect their lower incomes and their concentration in industries, such as the service sector, that often don't provide health benefits.

"Latinos realize that government will not fulfill every need, but what they admire about the United States is that the government steps in when there is a need," said Lorena Chambers, a Latina media consultant who worked on a campaign to help pass the president's health law.

Nearly half of Latinos in a recent Pew Research Center poll said they trusted the federal government to do the right thing "always" or "most of the time." Just 20% of white respondents felt that way. And two-thirds of Latinos believed the federal government should ensure that everyone has access to health insurance, a 2012 Latino Decisions survey found.

Challise Brittain, an unemployed teacher of Puerto Rican descent from Mississippi, said she was looking forward to getting health insurance under Obama's healthcare law next year. Brittain, 30, and her husband, an accountant, lost their jobs and their health coverage last year. Their two children, who are 2 and 4, qualify for Medicaid. Brittain responded to a Kaiser Family Foundation poll.

Republicans, she said, just don't seem to understand that kind of struggle. "It seems like whatever the president is for, they are against. They don't care about how that affects real people," she said.

The Republican National Committee acknowledged the damage caused by that perception in outlining its strategy to win over Latinos. "They want to know that we are not just the party for those at the top of the economic ladder because our dream of a better life is for them, too," party leaders wrote.

But Republicans show few signs of changing course on healthcare.

GOP lawmakers on Capitol Hill pushed more votes last month to repeal all or part of the law, after more than 30 such votes in 2011 and 2012. And the GOP budget just passed by the House would repeal the new health law and slash billions of dollars from future Medicaid spending, leaving tens of millions of mostly low-income Americans — many of them Latino — without health coverage.

Even two of the party's most prominent Latino politicians have taken up the repeal refrain.

Sen. Marco Rubio of Florida, considered a likely presidential contender, cited the law as an example of government hurting people in his GOP response to Obama's State of the Union speech in February. And newly elected Sen. Ted Cruz of Texas, a tea party favorite, used his first major speech on the Senate floor to push an amendment to defund the law.

noam.levey@latimes.com