The White House on Monday pushed President-elect Donald Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE not to reverse President Obama’s opening with Cuba, a final bid to protect one of Obama's top foreign policy accomplishments before he leaves office.

The effort took on new urgency Monday, when Trump threatened to “terminate” Obama’s decision to normalize relations with Cuba if the former Cold War foe refuses to “make a better deal” with the U.S.

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White House press secretary Josh Earnest cautioned that the incoming president could find it difficult to unwind the growing diplomatic, travel and business ties between the two nations.

“It’s just not as simple as one tweet might make it seem,” Earnest said, a dig at Trump’s preferred method of communication.

“There are significant diplomatic, economic [and] cultural costs that will have to be accounted for if this policy is rolled back.”

Earnest noted that Monday marked the resumption of direct commercial flights between the U.S. and Havana for the first time in half a century.

He also cited a spike in U.S. investments and travel opportunities allowed by new rules, which he said 50,000 Americans have taken advantage of in the last 18 months.

Earnest said “to cancel all of that would deal a significant economic blow” to Cubans who benefit from international travelers.

Trump’s comments put the two-year-old detente in jeopardy just days after the death of former Cuban leader Fidel Castro, which breathed new life into the policy debate.

They also came after a 45-minute phone conversation on Saturday between Obama and Trump.

It’s not clear what the two leaders spoke about, but Obama has publicly warned his successor that erasing his policies on healthcare and climate change could prove difficult.

Distancing the U.S. from Cuba would fulfill a campaign pledge and satisfy many of Trump’s Republican supporters, including Cuban-Americans in South Florida who favor a harder line against the government in Havana.

But it would be a major blow to Obama, whose administration worked for years to restore diplomatic relations with Cuba.

Obama and Castro’s younger brother, Raúl, the country’s current leader, announced in December 2014 that they would reestablish formal ties severed in 1961.

The two countries last year reopened long-shuttered embassies in each others’ capitals. Under the new policy, Americans can travel more freely to Cuba and bring back limited amounts of coveted consumer goods, such as cigars and rum.

The U.S. also raised caps on the amount of money Americans can send to their relatives in Cuba.

Trump has not specified exactly what changes Cuba would need to adopt in order to save the policy.

But aides to Trump say he wants to see Havana make fundamental reforms, such as opening up the economy and curbing political repression.

“There is going to have to be some movement from Cuba in order to have a relationship with the United States,” Reince Priebus, chairman of the Republican National Committee and Trump’s incoming chief of staff, said on “Fox News Sunday.”

Many Republicans, and some Democrats, have long said Obama has not done enough to force the Castro regime to improve the human-rights situation in Cuba, where dissidents are routinely jailed for speaking out against the government.

That criticism resurfaced this weekend when several Republicans slammed Obama for issuing a relatively anodyne statement on Castro’s death, which said the former leader “altered the course of individual lives, families, and of the Cuban nation.”

Sen. Marco Rubio Marco Antonio RubioOvernight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers Democrats step up hardball tactics as Supreme Court fight heats up Press: Notorious RBG vs Notorious GOP MORE (R-Fla.), a Cuban-American, called the statement “pathetic” and urged Obama not to send a delegation to Castro’s funeral on Sunday.

Earnest said Obama and Vice President Biden would not attend the ceremony but would not rule out the possibility of Secretary of State John Kerry John Forbes KerryThe Memo: Warning signs flash for Trump on debates Divided country, divided church TV ads favored Biden 2-1 in past month MORE traveling to Cuba for the funeral.

Earnest said Obama was not “whitewashing” Castro’s human-rights record and instead was trying to take a forward-looking approach to U.S.-Cuba relations.

Opponents of the policy, he said, are “scrambling to try to justify their loyalty to an obviously failed policy of isolation that didn't bring about any results for the Cuban people or for the American people.”

For Trump, rolling back the policies would not require an act of Congress, since Obama made them via executive actions. But it could still provoke a political fight with some Republican lawmakers and business groups that favor continued engagement with Cuba.

Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style MORE (R-Ariz.), a supporter of improved Cuba ties, urged Trump to change his views, saying the Castros used the old U.S. policy as “a convenient scapegoat for the failures of socialism.”

“I’ve always thought, if you want to punish the Castros, just make them deal with spring break once or twice,” Flake, a frequent Trump critic, said Monday on MSNBC’s “Morning Joe.”

The thaw is also popular with the public.

A CBS News/New York Times poll conducted ahead of Obama’s visit to the island in March showed 58 percent of Americans support reestablishing diplomatic relations with Cuba.