HAVANA — Donald Trump’s threat to undo President Barack Obama’s detente with Cuba unless President Raul Castro abides by Trump’s list of demands is provoking widespread anxiety among ordinary Cubans, who were paying little attention to the U.S. presidential campaign until now.

Trump had been generally supportive of Obama’s reestablishment of diplomatic ties and normalization of relations, saying he thought detente was “fine” although he would have cut a better deal.

Then, in Miami on Friday, the Republican nominee said he would reverse Obama’s series of executive orders unless Castro meets demands including “religious and political freedom for the Cuban people and the freeing of political prisoners.” Castro said in a speech the following day that Cuba “will not renounce a single one of its principles,” reiterating a longstanding rejection of any U.S. pressure.

While Hillary Clinton maintains an electoral college advantage, Cubans are suddenly envisioning the possibility of a U.S. president who would undo measures popular among virtually everyone on the island, from hard-line communists to advocates of greater freedom and democracy.

“I don’t think he’d make such a drastic decision. Or would he?” Bernardo Toledo, a 72-year-old retired state worker, asked nervously. “It would be disgraceful.”

While the detente announced on Dec. 17, 2014 has had limited direct impact on most ordinary Cubans, it has created feelings of optimism about a future of civil relations with Cuba’s giant neighbor to the north. An Univision/Washington Post poll of 1,200 Cubans taken in March, 2015 found that 97 percent supported detente.

For most ordinary people in a country that’s had only two leaders over nearly six decades, and where the president’s word is law, Trump’s unexpected reversal was a reminder that a single election might wipe away those closer ties.

“All we want is to be left in peace. Isn’t he thinking about our families?” complained pharmacist Heidi Picot. “How could he do something like this, make everybody worried?”

Still, some Cuban experts on relations with the U.S. saw the candidate as merely pandering to anti-Castro Cuban-Americans in South Florida, and don’t believe a President Trump would follow through with his campaign pledge. Detente is increasingly popular among Cuban-Americans and South Florida pollsters say Trump is not ahead with them by the margins managed by previous Republicans who’ve won Florida.

Hillary Clinton has declared her support for continuing Obama’s policy, which has reopened the U.S. Embassy, re-established direct flights and removed Cuba from a list of state terror sponsors. It also has done away with most limits on cash remittances from the U.S and increased cooperation on topics ranging from law enforcement to public health.

“I don’t think it will be very easy for Trump to reverse some things,” former diplomat Carlos Alzugary said. “Break diplomatic relations? Put Cuba back on the list of terrorist states? Those things are almost impossible.”

Cuba’s state media had been virtually silent on the U.S. presidential campaign, seemingly uncertain of how to square the polarizing and highly competitive race with the oft-repeated Cuban assertion that U.S. democracy offers false choices between nearly identical corporate pawns.

Trump’s statement generated an unusual amount of official coverage over the weekend. State radio stations and other government-run media accused the Republican of pandering to Cuban-Americans in an attempt to win Florida’s electoral votes.

A Trump reversal would fit a historical pattern, started under Jimmy Carter, in which Democratic presidents build ties to Cuba and their Republican successors largely undo them.

Obama has worked hard to make the opening irreversible by building popular and corporate support at home. In Cuba, the government has welcomed some new ties, like scientific cooperation and commercial flights. It has stalled on others, like ferries from Florida. Some observers believe that’s because Castro’s government fears building ties that a hostile future U.S. administration could use in the interests of regime change.

The Cuban government has given no indication of whether Trump’s statement will give new impetus to U.S.-Cuba normalization, or cause the process to stall in what could be its last three months.

Meanwhile, Cubans remain hopeful, but increasingly worried.

“It’s a way to move the economy forward, to diversify,” said Yenitsia Arango, a 34-year-old nurse. “The door’s been opened to better relations and it’s not a good idea to go in reverse.”

_____ Correspondent Michael Weissenstein contributed to this report.

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Andrea Rodriguez on Twitter: http://www.twitter.com/ARrodriguezAP

Michael Weissenstein on Twitter: http://www.twitter.com/mweissenstein