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CHICAGO, IL – While the country’s flailing economy is still shaping up to be the most important issue in next year’s election, the hot-button topic of immigration continues to play a prominent role in the Republican primary. Never has that been more apparent than today.

In Florida, Mitt Romney is trotting out a series of high-profile Cuban-American endorsements. In New Hampshire, Rick Perry is showcasing the support of anti-illegal immigration hardliner Arizona Sheriff Joe Arpaio. And in South Carolina, all the talk is about Newt Gingrich’s comments Monday backing the state’s strict new immigration law.

“We’ve seen a real devaluation, sadly, in how Republicans view the issue of how you deal with the undocumented, and they’re in a quite myopic way focused on enforcement-only policies,” Angie Kelley, vice president for immigration policy and advocacy at the Center for American Progress, said Tuesday on a conference call with reporters.

At last week’s debate, in Washington, D.C., Gingrich outlined a moderate immigration policy that his rivals quickly denounced as “amnesty.” If an immigrant has been here for a quarter of a century, raising a family, paying taxes and obeying the law, Gingrich said, then the government should not expel him or her.

“I’m prepared to take the heat for saying, let’s be humane in enforcing the law without giving them citizenship, but by finding a way to create legality so that they are not separated from their families,” Gingrich said.

And take heat he did, with rivals such as Romney arguing that the former House Speaker’s approach amounted to “amnesty.”

Romney has ripped Gingrich for proposing that a small number of the nation’s 11 million illegal immigrants — around two-thirds of whom have been living here for over a decade — be granted a path to legalization, but not citizenship. Seeking to combat the charges that he was soft on immigration, Gingrich this week came out in favor of South Carolina’s controversial law that would make traffic police contact federal immigration officials if they suspect that someone is in the country illegally.

“South Carolinians have actually passed a law that I think is a pretty reasonable law – that basically says, if you pull somebody over for legitimate reasons, you can ask them whether or not they’re a citizen,” Gingrich said Monday in Charleston. “This is the opposite of sanctuary states. Think of it as enforcement society rather than a sanctuary society.”

However, critics of South Carolina’s controversial new law have contended that it amounts to racial profiling. South Carolina has become only the latest in a growing line of states who have taken the immigration battle into their own hands, following similar actions in Alabama and Arizona.

“He was throwing down his unconditional support for anti-immigrant laws in Alabama and South Carolina and accusing President Obama of being more supportive of Mexico and, you know, being rather incendiary but not really offering any smart solutions,” Kelly said.

While Romney was hammering Gingrich for not being tough enough on immigration, the former Massachusetts governor was touting his own foreign policy boost. In Miami on Tuesday, Romney secured three key Cuban-American endorsements: U.S. Reps. Ileana Ros Lehtinen and Mario Diaz-Balart, and the latter’s brother, former Congressman Lincoln Diaz-Balart.

“They’re conservative leaders who will help me articulate my vision to make America more prosperous at home and respected throughout the world,” Romney said in a statement.

In 2008 the trio backed the Republican who beat Romney for the GOP nomination: Sen. John McCain. In addition, all three of them support the DREAM Act, the Democrats’ bill that would help undocumented students who came to this country before age 16 become legal residents after five years by completing higher education or military service. Despite enjoying widespread support among all voters, the bill was shot down by Senate Republicans last fall. Romney opposes the measure, but despite their differences, he won the endorsements of the Cuban-American trio.

“There’s an interesting contradiction there,” Kelly said Tuesday.

In Florida, a key state both in the Republican primary and the general election , the Cuban vote could prove crucial. Around 540,000 of Florida’s 1.5 million Latino voters are of Cuban origin, a group mostly based near Miami. Florida is set to vote fourth in the primary season on Jan. 31.

Before Florida takes its turn in the primary, New Hampshire will have its say. And on Tuesday the Granite State was where Rick Perry — who has also been blasting Gingrich on immigration — rolled out his support of Arpaio, the controversial sheriff of Maricopa County in Arizona who calls himself America’s Toughest Sheriff.

“I call this a horrific policy, but the Obama administration has a catch-and-release policy where nonviolent illegal aliens are released into the general public today. My policy will be to detain and to deport every illegal alien that we apprehend. That is how we stop that issue,” Perry said at a campaign stop in New Hampshire .

“The federal government has failed on border crime and border enforcement, and no candidate for president has done more to secure the border than Governor Rick Perry,” Arpaio said in a statement.

It is indisputable that no other candidate has as extensive an immigration record as Perry, but whether or not that helps or hurts the Texas governor remains to be seen.

In Texas, Perry signed a voter ID law, vetoed a bill that would allow illegal immigrants to obtain driver’s licenses and sent $400 million to the border in the form of Texas Ranger reconnaissance teams. Perry differs from the rest of the GOP field as he opposes the construction of a fence along the entire U.S-Mexico border and instead believes the fences should be concentrated in metropolitan areas.

Earlier this fall, Perry caused an uproar when he suggested that people who oppose granting in-state tuition to illegal immigrants “don’t have a heart,” a comment he later walked back.

The support of Arpaio — who takes a hard-line stance on illegal immigration, leading raids to round up and jail illegal immigrants, and was a major proponent of the controversial Arizona immigration law — was highly coveted in the Republican race. He met Rep. Michele Bachmann in September and Herman Cain in October and he has spoken over the phone with Romney, whom he endorsed in 2008 over McCain.

With immigration such a key issue in the 2012 race, there is a lot at stake here. Latinos are the fastest-growing voting group in the nation and they are set to hit the polls next fall more than ever before, with a predicted turnout of about 12 million. Latinos tend to vote Democratic — in 2008 Obama won two-thirds of the Latino vote nationwide and he continues to enjoy sizable leads over his potential GOP opponents among Latinos . The Republican candidates’ stances on immigration are unlikely to help them bridge that gap.

“You have Gingrich with a very limited program saying maybe a few will be able to get legal status and Romney calling that amnesty. The lurch to the right by the Republicans in recent years seems to me to create a huge problem for them when they come out of the primary and into the general, no matter who the nominee is,” said Frank Sharry , executive director of America’s Voice.

In his role as head of Latino Decisions, Gary Segura, a professor at Stanford University, has conducted extensive polling on public sentiment about immigration reform, most recently a Nov. 8 poll for Univision.

“Among all voters, 58 percent of registered voters favored a pathway to citizenship and obviously a larger percentage of Latinos favored that position. On the opposite end of the spectrum, about 25 percent of all voters favored the most punitive policy, which is deportation and treatment as felons,” Segura said. “So we actually have a really interesting pattern here where the majority position of voters in the United States is one that favors a pathway to citizenship.”

Matthew Jaffe is covering the 2012 campaign for ABC News and Univision.