The relationship between Texas Gov. Rick Perry and former Massachusetts Gov. Mitt Romney may get a lot more disagreeable.

Story highlights

The GOP holds the third presidential debate in as many weeks

Perry advisers argue that Romney sounds like a Democrat

Two new polls show former Utah Gov. Jon Huntsman climbing into double digits

Orlando CNN  — 

Here are four things we learned from Thursday night’s Republican Party of Florida/Fox News/Google debate in Orlando, the third GOP presidential debate in as many weeks:

The battle over Social Security is far from over

The controversial entitlement reform plan drafted by House Budget Chairman Paul Ryan and supported by many Republicans has given Democrats plenty of reasons to think that they can exploit issues like Social Security and Medicare in a retiree-heavy state like Florida once the general election rolls around.

But who would have thought Social Security would be a central issue in a Republican primary?

Former Massachusetts Gov. Mitt Romney has been thumping Texas Gov. Rick Perry for weeks on the topic, highlighting passages in Perry’s book “Fed Up!” that seem to question why Social Security is a federal program.

In a state like Florida, with nearly 4 million citizens who depend on Social Security, the issue could be political gold for Romney.

But Perry advisers argue that Romney sounds like a Democrat by using Social Security as a cudgel against someone in his own party.

Florida state Sen. John Thrasher, a leading Romney supporter in the state, said Republican primary voters care deeply about the program even while wanting to see it reformed.

Even though Romney was jeered at times when he pressed the attack, Thrasher said he should keep it up.

“These are hardcore Republicans and they believe in Social Security,” Thrasher said. “I think Romney should keep his foot on Perry’s neck on that issue.”

This Perry-Romney thing could get nasty

The two front-runners for the Republican nomination mixed it up repeatedly throughout Thursday’s debate in a series of sharply worded exchanges about Social Security, immigration and health care reform.

And that was before Perry accused Romney of being a flip-flopper on Second Amendment rights and abortion, a charge that dogged Romney throughout his failed 2008 presidential bid.

Their relationship may not be as frosty as the one between Romney and Arizona Sen. John McCain during the closing months of the 2008 Republican primary, but it seems increasingly clear that there is no love lost between Perry and Romney.

That mutual distaste is almost certain to grow in the coming weeks

After the debate, Romney adviser Eric Fehrnstrom even went so far as to compare Perry to President Barack Obama.

“Rick Perry is very similar to President Obama in that neither one has the skills to lead on the economy,” Fehrnstrom told reporters. “This is what distinguishes Mitt Romney not only from Rick Perry and President Obama but from every other candidate in the Republican field.”

Perry’s campaign manager Rob Johnson called that accusation “ridiculous.”

Huntsman is feeling good

Two new polls showing former Utah Gov. Jon Huntsman climbing into double digits in New Hampshire – a must-win state for Huntsman on the path to the GOP nomination – appear to have given him a spring in his step.

Huntsman was underwhelming in two earlier debate performances, but on Thursday he delivered a genial and confident performance that highlighted his foreign policy experience.

In an exchange with former Pennsylvania Sen. Rick Santorum on the topic of scaling back American operations in Afghanistan and Pakistan, Huntsman leaned into the microphone and pointed out that “that he is the only one on stage with any hands-on foreign policy experience.”

And he won applause from the crowd when he said the country should wind down its overseas commitments.

“At the end of the day, only Pakistan can save Pakistan,” he said. “Only Afghanistan can save Afghanistan. All I want is for America to save America.”

He also seemed happy to let Romney and Perry drag each other down with their attacks.

“I wasn’t part of the book club tonight,” he told reporters after the debate, referring to the Romney-Perry scuffle. “I was offering real solutions.”

Santorum looks stronger

Despite visiting key caucus and primary states of Iowa and South Carolina more than any other GOP presidential candidate, Santorum has remained something of an asterisk throughout the campaign.

But impressive performances in consecutive debates may begin to change that.

An unapologetic social conservative, Santorum aggressively attacked Perry from his right flank and seemed to get under his skin when he asked why the governor signed a 2001 bill that gave tuition breaks to the children of illegal immigrants.

“Santorum made himself relevant,” said Florida Senate President Mike Haridopolos, who is neutral in the 2012 race. “He is helping his cause because he is being so straightforward, and I think that matters a lot in politics where people are turned off by the fluff. He really put Gov. Perry on the defensive on illegal immigration tonight and it made it tough for Perry to gain the strength that he thought he would have tonight.”