Cuban-Americans historically are a reliable vote bank for Republicans who toe a hard line on Cuba, but now a group of GOP congressmen are pushing to take away policies they call “amnesty” for people who leave the authoritarian island.

Leading a long-shot effort to undo the “wet foot, dry foot” policy that allows Cubans who reach U.S. territory to stay and to repeal the Cuban Adjustment Act that fast-tracks benefits and residency rights is Rep. Paul Gosar, R-Ariz.

Gosar and his peers consider the policies for Cubans outdated, given the recent thaw in relations.

“When you all the sudden are normalizing relations with Cuba you have to end these incentives,” he says, pointing to an upswing in arrivals.

He says many Hispanic residents in his district who aren’t from Cuba “feel like, ‘Woah, woah, woah, why does someone need to go to the front of the line just because they’re Cuban?’”

“We need to treat everyone fairly," he says.

The number of Cubans entering the U.S. has grown – 60 percent along the Texas border, according to U.S. Customs and Border Protection – since President Barack Obama announced in December the normalization of relations with Cuba.

And not all Cubans given permanent residency stay in the U.S., an investigation by the Florida Sun-Sentinel recently found, with many living the majority of the time in Cuba while collecting U.S. food stamp, disability and welfare benefits.

Gosar says “rampant fraud” by Cubans who are “taking their welfare checks and living a little bit higher on the hog in Cuba” is a good reason to pass his bill.

He and eight other Republicans in the House of Representatives on Friday introduced the Ending Special National Origin-Based Immigration Programs for Cubans Act of 2015.

The bill’s repeal of the Cuban Adjustment Act of 1966 would end the automatic right to benefits and permanent residency after one year for Cubans living in the U.S. Refugees and asylum recipients get similar treatment, but Cubans do not need to prove they risk persecution. Other immigrants must enter the country legally and cannot collect benefits for years.

The bill expresses the sense of Congress that the “wet foot, dry foot” policy is null and void and would ban use of funds to implement an immigration scheme enacted in 2007 that allows entry of Cubans with U.S. citizen or permanent resident relatives.

The legislative push was unveiled rebuking the status quo as "amnesty," a dirty word among Republicans who control both chambers of Congress. Gosar said in an initial statement the bill would “end the outdated policies that provide amnesty to Cuban aliens and criminals."

A wholesale repeal of special treatment for Cubans, however, would not be taken kindly by critics of the Castro government.

“Until Cuba is a democracy, people should be treated as refugees” says Omar Lopez, who deals with human rights issues for the Cuban American National Foundation.

The gush of new Cuban immigrants to the U.S. – an increase Lopez pegs at about 50 percent – shows the Castro government continues to repress its citizens, he says.

“There are a lot of people abusing the privilege of the benefits the Cuban community receives,” Lopez concedes, and “the congressmen have a point when they say people are abusing this policy. But when someone arrives you don’t know they are going back to Cuba."

Lopez says it might be reasonable to make some reform to shield against benefit-collectors who return to Cuba, a sentiment that has been voiced by other Cuban-American leaders.

In fact, one Cuban-American congressman, Rep. Carlos Curbelo, R-Fla., has been vocal about the need to implement reforms.

“While our Cuba policy should continue to provide an expedited path to freedom for Cubans facing political persecution, it is evident that the existing framework under the Cuban Adjustment Act is flawed and requires reform,” he says.

“Since January of this year, I have been working on a bipartisan solution with a chance of being signed into law,” Curbelo says. “Those efforts are progressing, and they will continue.”

Gosar, who says he opposes the thaw in U.S.-Cuba relations, sees his role as staking a position that will spark a more expansive debate – something he sees himself as excelling at in Congress.

“The Florida delegation is sometimes a little more deferential because they have a huge Cuban bloc in there, and sometimes change is better initiated outside that bloc,” he says.