President Obama’s surprising move toward normalizing relations with Cuba amounts to a big bet that the nation – and the crucial swing state of Florida – has turned a political corner from the Cold War era.

Obama’s decision aligns with a growing sentiment that current Cuba policy has become counterproductive. Among those making that argument has been former secretary of state Hillary Rodham Clinton, who is presumed to be the front-runner for the 2016 Democratic presidential nomination.

But the new stance immediately came under challenge. Many leading Republicans – and one Democratic senator – denounced the president as feckless, overreaching and naive in his negotiations with the government of President Raul Castro, the brother of longtime leader Fidel Castro.

“This entire policy shift announced today is based on an illusion, on a lie, the lie and the illusion that more commerce and access to money and goods will translate to political freedom for the Cuban people,” said Sen. Marco Rubio, a Florida Republican, who is considering a presidential bid and whose parents emigrated from Cuba in the 1950s. “All this is going to do is give the Castro regime, which controls every aspect of Cuban life, the opportunity to manipulate these changes to perpetuate itself in power.”

Former Florida governor Jeb Bush – considered the 2016 Republican front-runner after announcing an exploratory bid Tuesday – had called for strengthening the embargo against Cuba as recently as two weeks ago.

On his Facebook page Wednesday, Bush wrote that the administration’s decision to restore diplomatic ties with Cuba is “the latest foreign policy misstep by this President, and another dramatic overreach of his executive authority. It undermines America’s credibility and undermines the quest for a free and democratic Cuba.”

Among other possible Republican 2016 presidential candidates, Sen. Ted Cruz of Texas and Rep. Paul Ryan of Wisconsin criticized Obama on Cuba, while Sen. Rand Paul of Kentucky and New Jersey Gov. Chris Christie and several others were quiet.

Democratic Sen. Robert Menendez of New Jersey, a longtime hawk on Cuba policy, said the president’s move was “misguided and fails to understand the nature of the regime in Cuba that has exerted its authoritarian control over the Cuban people for 55 years.”

The bulk of the criticism suggested that, for now at least, the conservative base remains firmly committed to keeping Cuban relations in the deep freeze where they have been for half a century. That position, however, is increasingly at odds with the view of the electorate at large.

More than a decade ago, polls began showing a tilt in public sentiment toward normalizing ties with the island 90 miles from the tip of Key West, Florida. In 2009, a Washington Post-ABC News survey found that two-thirds of Americans supported restoring diplomatic relations with Cuba, while only 27 percent opposed doing so.

The old ideological and economic battle lines have also been fading on the ground. Even as a trade embargo has remained in place, nearly 600,000 U.S. travelers went to Cuba last year – the majority of them Cuban-Americans. Business interests have pushed for more openness, and the U.S. Chamber of Commerce pledged its support for Obama’s decision.

“Public opinion in Florida and in the country is moving to moderation on Cuba, and Obama is effectively using his political capital to make a long anticipated shift that history and the U.S. public will support,” Ted Piccone, a senior fellow with the Brookings Institution’s Latin America Initiative, wrote in an email from Havana.

While the Cuban-American population has long been identified with the Republican Party, that allegiance has shifted.