President Obama’s surprising move toward normalizing relations with Cuba amounts to a big bet that the nation — and, particularly, 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, the presumed front-
runner for the 2016 Democratic presidential nomination, who said the new stance has the potential to “encourage real and lasting reforms for the Cuban people.”

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 Raúl Castro, the brother of longtime Cuban 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 (R-Fla.), 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 GOP’s 2016 front-runner after announcing an exploratory bid Tuesday — had called for strengthening the embargo against Cuba as recently as two weeks ago.

In less than two minutes, here are the key moments from President Obama's speech about changes to relations with Cuba on Wednesday. (Sarah Parnass/The Washington Post)

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, New Jersey Gov. Chris Christie and several others were ­quiet.

The bulk of the GOP comments suggested that, for now at least, the conservative base remains firmly committed to keeping relations with Cuba 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, Fla. 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 e-mail from Havana.

Although the Cuban American population has long been identified with the Republican Party, that allegiance also has shifted. The change is largely generational, with those two or three generations removed from the ones who fled Castro’s regime in the 1950s and 1960s more open to voting Democratic.

More than 50 years after the U.S.-imposed embargo, President Obama has announced an effort to normalize ties with Cuba.

In 2012, Obama won the vote of Cuban Americans nationally by two percentage points and took a majority of their votes in Miami. He also won Florida twice — the second time after loosening some travel and other restrictions involving Cuba in his first term.

But Republican political consultant Alex Castellanos said Obama’s latest initiative will add fuel to arguments that he has lacked steadiness and strength in international relations, potentially elevating foreign policy as an issue in 2016.

“Weakness invites the wolves,” Castellanos said. “This is a president whose naivete is dangerous, who sees the world as he wishes it were and not as it is.”

As recently as the mid-1990s, the conventional wisdom was that no presidential candidate could hope to carry Florida unless he took a hard line on Cuba.

Former president Bill Clinton recalled in his memoir, “My Life,” that after Cuba shot down two civilian planes flown by an anti-Castro group, he signed the 1996 Helms-Burton Act stiffening the embargo, even though he had misgivings about the effect it would have on his ability to press the Cuban government for reform.

Now his wife, Hillary, is considered the leading contender for the 2016 Democratic nomination if she decides to run.

Cuba’s release of Alan Gross, a U.S. Agency for International Development contractor who was imprisoned for five years, was the achievement of a goal that Clinton had sought in public and in private during her tenure at the State Department.

In a statement Wednesday, Clinton said, “I am deeply relieved by Alan Gross’s safe return to the United States. . . . It is great news that Alan is finally home with his family, where he belongs.”

In her memoir, “Hard Choices,” released in June, Clinton blamed the Cuban government for making the case so difficult to resolve.

“It is possible that hard liners within the regime exploited the Gross case as an opportunity to put the brakes on any possible rapprochement with the United States and the domestic reforms that would require,” she wrote.

Clinton’s statement Wednesday also said, “I support President Obama’s decision to change course on Cuba policy, while keeping the focus on our principal objective — supporting the aspirations of the Cuban people for freedom.”

She said: “Despite good intentions, our decades-long policy of isolation has only strengthened the Castro regime’s grip on power. As I have said, the best way to bring change to Cuba is to expose its people to the values, information, and material comforts of the outside world.”

In “Hard Choices,” Clinton wrote that she had recommended to Obama that he review the embargo.

“It wasn’t achieving its goals and it was holding back our broader agenda across Latin America,” Clinton wrote. “After twenty years of observing and dealing with the U.S.-Cuba relationship, I thought we should shift the onus onto the Castros to explain why they remained undemocratic and abusive.”

The work of opening diplomatic and economic ties severed for more than 53 years will probably carry into the next presidency, particularly if the Republican-led Congress ties up the most meaningful ele­ments of an embargo repeal.

Only a few Democrats signaled disagreement with Obama’s decision. 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.”

Former Florida governor and senator Bob Graham, a revered elder in state Democratic politics, also expressed misgivings. He said in an interview that he would have preferred moving toward normalizing relations “on a more incremental basis.” The administration “went for the long play” instead, he said.

“We’re in a situation now where we have made a very generous offer to the Cuban government and don’t have leverage to make sure that those commitments filter down to the Cuban people,” Graham said.