MIAMI – As they jockey for possible presidential bids, Republican senators Marco Rubio and Rand Paul are taking aim at each other on TV, Twitter and Facebook over Cuba policy.

Rubio, a Cuba hard-liner from Florida, attacked President Obama's effort to re-establish ties with Cuba. Paul, the pugnacious Kentuckian, thinks Obama was right.

"He doesn't know what he's talking about," Rubio promptly said of Paul in a TV interview.

"Senator @marcorubio is acting like an isolationist who wants to retreat to our borders and perhaps build a moat," Paul fired back on Twitter "I reject this isolationism."

The unexpected donnybrook exposed a latent tension in the Republican Party, with Rubio representing the conservative mainstream establishment and Paul playing the role of libertarian.

Even if the two don't run against each other, the conflict could presage trouble in the U.S. Senate's GOP caucus, which is now in the majority. Incoming Majority Leader Mitch McConnell said he supports Rubio's hard line on Cuba, but he has said that he backs his fellow Kentucky senator for president. Adding to the drama, Tea Party Sen. Ted Cruz of Texas might run for president as well.

The conflict between Paul and Rubio erupted a day after Obama and Raul Castro jointly announced efforts to normalize relations. Rubio quickly became a fixture in the news media as he led the GOP efforts to criticize what he describes as a capitulation by Obama.

Rubio, other Republicans and Cuban-American lawmakers have vowed to use Congress' power of the purse strings and confirmations to fight Obama's efforts.

Taking opposite sides

But while Republican presidential candidates lined up to echo Rubio's position, Paul sided more with Obama, noting many U.S. farmers support the idea of more Cuba trade because it's a new market for their crops.

"The 50-year embargo just hasn't worked," Paul said in a radio interview with a Huntington, W. Va., station. "If the goal is regime change, it sure doesn't seem to be working, and probably it punishes the people more than the regime because the regime can blame the embargo for hardship."

Paul pointed out that many younger Cuban-Americans support his point of view, which polls indicate is true.

Later that evening, on Fox News, Rubio blasted Paul for being ignorant.

"Like many people, he has no idea what he's talking about," snapped Rubio. "I would expect that people would understand that if they just took a moment to analyze that, they would realize that the embargo is not what's hurting the Cuban people. It's the lack of freedom and the lack of competent leaders."

Rubio went on to explain that the embargo has numerous "holes in it" and has not been a true embargo. So it hasn't failed, contends Rubio, because it has never fully been in force.

Then Paul hit back on Facebook: "Seems to me, Senator Rubio is acting like an isolationist who wants to retreat to our borders and perhaps build a moat. I reject this isolationism. Finally, let's be clear that Senator Rubio does not speak for the majority of Cuban-Americans."

Soon after that comment, Paul started to address Rubio on Twitter. "Hey @marcorubio if the embargo doesn't hurt Cuba, why do you want to keep it?" Paul asked first.

Then he added, "@marcorubio what about the majority of Cuban-Americans who now support normalizing relations between our countries?" including a link to a story concerning a poll this summer about Cuban-American attitudes. Rubio didn't respond.

Instead, CNN commentator and Florida resident Ana Navarro chimed in on Twitter, noting that Paul, an eye doctor, "may know more re glaucoma & cataracts than Rubio, but trying to debate Marco on Cuba is shortsighted. He's playing out of his league."

Bush, Jindal weigh in

Other potential Republican 2016 contenders, former Florida Gov. Jeb Bush and Louisiana Gov. Bobby Jindal slammed the White House's shift in policy.

Bush, who recently reaffirmed his support for the U.S. trade embargo against Cuba, said Obama's decision undermined efforts to create a free and democratic Cuba. He accused Obama of rewarding dictators "with a disastrous human rights record."

On the other side of the 2016 presidential arena, Democrat Hillary Clinton praised the Obama administration's move to normalize relations with Cuba and reiterated her view that the U.S. should lift the trade embargo.

Cuba policy matters to voters, particularly in Florida, which has 29 of the 270 Electoral College votes it takes to win the presidency.

A Pew Research Center analysis of 2013 survey data found that less than half of registered Cuban-American voters lean Republican, compared with 64 percent a decade ago. During the same time period, the share of Cubans who support Democrats has doubled from 22 percent to 44 percent.