Under the revised travel policy, US officials say there will be tighter enforcement to make sure Americans legally fit the 12 authorized categories they claim to be traveling under, which could spook many visitors, wary of receiving a hefty fine.
"All the Trump administration is saying is, 'there's one thing we're going to change, and that is we're no longer going to permit individual travelers to purport to be traveling to Cuba under the education exemption, '" said Harry Clark, a partner at Orrick and chair of the law firm's worldwide trade and compliance group.
"I think it is a step in the right direction that the Trump administration is going to follow the immigration laws that have been passed by Congress and are on the books and it's not going to continue President Obama's illegal executive amnesty in the DAPA program", said Senator Ted Cruz, R - Texas.
The lengthy statement went on to strike a conciliatory tone, saying Cuba wants to continue negotiations with the United States on a variety of subjects.
As word of Trump's proposals began to emerge this week, Benjamin Rhodes, a former senior Obama official who negotiated much of the thaw with Cuba, said it was important to focus on what would "not change" including diplomatic relations, bilateral cooperation in areas such as narcotics trafficking and immigration. United States airlines and cruise ships will still be allowed to serve the island.
In fact, Trump is getting bipartisan support for his call to bring back Shakur to USA soil. "As someone who had the privilege of traveling to Cuba with President Obama, I saw firsthand how the country has a desire for openness and information".
Some 285,000 people visited the Caribbean country in 2016, up 74 per cent over 2015, with Americans the third-biggest group after Canadians and Cuban expats.
The policy also allows Americans to continue patronizing state-run hotels and other businesses that are not directly linked with Cuba's military and state-security services.
But individual "people-to-people" trips by Americans to Cuba, allowed by Obama for the first time in decades, will again be prohibited. Florida is the place where all the emigres settle, and they turned to vote Trump a year ago. He said that Trump is not changing or not completely reversing the open-hand policies of Obama. "Why would you go back to a policy that has failed for 55 years?"
Havana considers the new policy driven by Trump to be a "hardening of the blockade (...) which not only causes damage and deprivation to the Cuban people and constitutes an undeniable obstacle to the development of our economy, but also affects the sovereignty and interests of other countries".
"The government of Cuba denounces the new measures toughening the embargo", Cuban state TV said. Obama and his aides argued that commerce and travel between the countries, which has blossomed since he relaxed the rules, would make his policy irreversible.
Trump during his speech in Miami slammed Cuba, saying, "The Castro regime has shipped arms to North Korea and fueled chaos in Venezuela". Outside of Miami, Trump faced opposition in the US agricultural sector.
Weissenstein reported from Havana and Lederman from Washington.