U.S. President Barack Obama’s decision to restore diplomatic ties with Cuba may have altered the course for the historically frozen relationship, but for now the change still doesn’t amount to much for Cuban immigration to the U.S. Still, that hasn’t stopped rumors that preferential treatment for immigrants from Cuba might soon end -- leading to desperate attempts by some to reach American soil by boat.

The U.S. Coast Guard reported last week that it was seeing an uptick in the number of migrants trying to reach the U.S. by sea, a trend that began in mid-December, around the time President Obama and President Raul Castro made their historic announcement to resume ties.  The Coast Guard said it intercepted 481 Cubans immigrating to the U.S. by boat in December, a 117 percent increase from the same period in 2013.

The reason, it said, was a wealth of new rumors that the so-called “wet foot, dry foot” policy, which allows Cubans permission to stay in the U.S. if they reach its shores, was in its final days. The Coast Guard issued a statement last week to clarify that the Obama administration announcement on U.S.-Cuba ties had no implications for a change in Cuban immigration policy, which can only be done as a result of congressional action.

The new Republican-dominated Congress has the power to repeal the embargo on Cuba, the last legislative hurdle to restoring full relations with the United States. But those prospects look dim, and Cuban-American members of Congress who have traditionally supported the embargo, including Sen. Marco Rubio, R. Fla., and Rep. Ileana Ros-Lehtinen, R-Fla., have signaled a coming fight over appointing an ambassador to the new U.S. embassy in Havana. But the situation is somewhat different when it comes to policies governing Cuban immigration.

Since the embargo came into force, U.S. immigration policy on Cuba has been guided by the 1966 Cuban Adjustment Act, which allows Cuban immigrants an opportunity to apply for U.S. citizenship a year after their arrival. The “wet foot, dry foot” policy was attached as an amendment to the law in 1995. No other immigrant group receives the same privileges. While both policies are popular among Cuban-Americans – a 2014 survey by the Cuba Research Institute at Florida International University found that 86 percent of Cuban-Americans in Florida’s Miami-Dade County strongly supported the Cuban Adjustment Act, with 63 percent approval for the “wet foot, dry foot” policy – elements of these policies have come under scrutiny in recent years.

Some critics have pointed to the Cuban Adjustment Act as unfair preferential treatment for Cuban immigrants, while others have decried abuse of the system. Last week, Florida’s Sun Sentinel newspaper unveiled an in-depth investigation of criminals’ use of the law to funnel illicit money to and from Cuba. In 2013, when Congress was debating a bipartisan bill on comprehensive immigration, Rubio indicated he wanted to “re-examine” the Cuban Adjustment Act as well, saying it was attracting some economic migrants who would simply return to Cuba for visits after securing their U.S. citizenship.

“I don’t criticize anyone who wants to go visit their mom or dad or their dying brother or sister in Cuba,” he said at the time, according to the Tampa Bay Times. “But I am telling you it gets very difficult to justify someone’s status as an exile and refugee when a year and a half after they get here they are flying back to that country over and over again.”

It might seem like a prime occasion for lawmakers to address Cuban migration, given that U.S.-Cuba policy and immigration reform are hot topics for Congress right now. But Benjamin Bishin, a professor of political science at the University of California at Riverside and analyst of Cuban-American politics, said he doubted any changes were forthcoming.

“While there is lots of publicity right now, Republicans are still split on the issue, and the Cuba lobby has a lot of influence in Congress,” he said.

“Because it is so easy to prevent legislation from being passed or changed in Congress, I think it will take overwhelming support before we see explicit legislative changes,” he added. “And this isn’t an issue the GOP is in a rush to deal with.”