By Marilia Brocchetto and Darran Simon

CNN

(CNN) -- Laura Vianelo remembers the stories of young Cuban migrants who "threw themselves at the sea," only to die in a desperate attempt to set foot on American soil.

So, she applauded the Obama administration's abrupt end to the longstanding policy, known as "wet foot, dry foot." The policy encouraged Cubans to risk their lives to seek freedom and enter the US without a visa to become permanent residents, she said.

"It is now up to the new generation, the young Cubans, to liberate themselves from communism the way it's supposed to be done, from inside Cuba," Vianelo said.

She was among scores of Cuban Americans who gathered Thursday at the popular Versailles Restaurant in Miami's Little Havana neighborhood to discuss the policy change. Some expressed displeasure. Others said the change could ultimately be a boon for the island nation.

The "wet foot, dry foot" policy, in place for more than two decades, had applied solely to Cubans. Following a mass exodus of Cubans to the United States, former President Bill Clinton in the mid-1990s changed the "open door" policy on Cuban refugees -- first established by President Lyndon B. Johnson -- to the "wet, foot, dry foot" policy that repatriated Cubans intercepted at sea but allowed those who reach land to stay.

Other immigrants, like Haitians, who have been arrested and deported if they entered the country without a visa, have long criticized the policy.

Treating Cubans like other migrants

Orlando Silva, a Miami doctor who fled Cuba with his family and never went back, said the policy change "is another betrayal by this country" that favors communism.

The United States has "always been against this country," he said of his native homeland.

A senior administration official said the US Department of Homeland Security would eliminate the policy that made Cuban nationals eligible for resident status within a year.

Immediately, Cubans "who attempt to enter the United States illegally and do not qualify for humanitarian relief will be subject to removal, consistent with US law and enforcement priorities," the White House said in a statement.

"By taking this step, we are treating Cuban migrants the same way we treat migrants from other countries," the statement said.

Medical parole program also eliminated

Cuba's government also agreed to accept Cuban nationals who have been ordered removed from the United States, just as they had accepted migrants intercepted at sea under the "wet foot, dry foot" policy, the White House said.

The Department of Homeland Security also eliminated a policy for Cuban medical professionals known as the Cuban Medical Professional Parole Program, a senior administration official said.

Miami-Dade County, Florida, Mayor Carlos A. Gimenez, whose county boasts a large Cuban-American population, said he was disappointed by the decision to end the medical parole program.

"The duties of the doctors who were previously protected by this program will continue to be mandated by the Cuban dictatorship," Gimenez said in a statement. "These doctors have been used as instruments of the regime and sadly, the elimination of the program will negatively impact their ability to practice medicine freely.

Gimenez also said eliminating the "wet foot, dry foot policy" would "undoubtedly impact" the Cuban-American community. But while the old policy granted relief to many fleeing persecution, the mayor said he was concerned it "was being abused and required adjustments."

Family Reunification Parole Program unaffected

Federal officials said the DHS is also eliminating an exemption that had prevented the use of expedited removal proceedings for Cuban nationals apprehended at ports of entry or near the border.

The existing Cuban Family Reunification Parole Program, which allows certain eligible US citizens and lawful permanent residents to apply for parole for their family members in Cuba, is unaffected, the official said.

The "wet foot, dry foot" change was likely to be Obama's last move in his historic dealings with Cuba, In 2014, Obama reopened ties to the island nation after a half century of frozen diplomatic ties.

Could real change now come to Cuba?

In November, Cuba's longtime leader Fidel Castro died at age 90. Castro's younger brother, Raul, who had been running the island nation for more than a decade, plans to step down in 2018.

Music producer Armando Flores, a second-generation Cuban, said the "wet foot, dry foot" policy was "an escape valve" for Cubans under the Castro regime. But the policy change may bring out transformation of the government, he said.

"Lots of things can happen, like a rebellion or a bigger focus on these Cubans that want to make a profound and real change in Cuba now that this bridge isn't there... there's no escape," he said.

But Flores said it is now "unfortunate for those who really come to the US looking for liberty and ... find themselves in this situation."

CNN's Elise Labott, Kevin Liptak and Patrick Oppmann contributed to this report.