"On the one hand, you have the Reagan revolution," Thompson said during the debate. "You have the Reagan coalition of limited government and strong national security. On the other hand, you have the direction that Gov. Huckabee would take us in. He would be a Christian leader, but he would also bring about liberal economic policies, liberal foreign policies. .. That's not the model of the Reagan coalition. That's the model of the Democratic Party."
Huckabee didn't respond much during the debate, but appearing on MSNBC's "Morning Joe" Friday morning, he took his well-known wit literally below the belt, joking, "I think Fred needs some Metamucil. I think it would help a lot. He was in a bad mood last night."
Campaigning Friday in Michigan, Huckabee went on the attack more substantively.
"It was real interesting hearing Fred Thompson talk about Ronald Reagan last night," Huckabee said. "Because Fred Thompson supported [then-President] Gerald Ford in 1976 and not Ronald Reagan. He supported [then-Sen.] Howard Baker in 1980 and not Ronald Reagan. I appreciate his recent conversion, but some of us were for Ronald Reagan back in the early days; our legacy goes back a little further."
Huckabee also tried to paint Thompson as having been an undistinguished senator.
"Eight years is a pretty long time to get a check from the federal government and not be able to say" he was responsible for any major legislation, Huckabee said.
On Saturday, Thompson called the criticism of his previous support of Ford and Baker as "kind of silly. Howard Baker was my mentor and personal friend in Tennessee for years and years. If you check the record, Gov. Huckabee supported Democrats on a fairly consistent basis in his days in Arkansas politics. I don't think he wants to get into that discussion. We'll see."
Of Huckabee's Metamucil's joke, on Sunday morning Thompson said "his response was to return fire with some potty humor. That's the best he could come up with for the last three days."
He added that he was happy to compare his record to Huckabee's, whom he described as "having raised taxes $500 million more than he cut." He described Huckabee's criticisms of the Bush administration as "blame-America-first comments," and pointed out, correctly, the Huckabee campaign chairman Ed Rollins had called the Reagan coalition dead.
Huckabee, Thompson charged, "talked around the subject and smiled and giggled and told a couple of jokes. When I came back, I said, 'You know, this is about the heart and mind of the Republican Party, because I don't believe it [the Reagan coalition] is [dead].'"
Said Huckabee, "The Writers Guild strike needs to end soon. Fred's got to get some better lines. Calling me a liberal would be laughable in Arkansas, where people recognized -- if anything, they called me this ultra-conservative guy. ... It's always interesting to me, when people get desperate, they start grabbing for anything."
Thompson responded that he had been asking questions about Huckabee's support for closing down the prison at Guantanamo Bay, his support for public programs for the children of illegal immigrants, and the fact that he was endorsed by a teachers' union.
"These are substantive issues," Thompson said. "These are not personal attacks. If the governor wants to get into personal attacks and things that happened some years ago and things that they've done and allegations, there's enough on the record in Arkansas that will keep us busy for the rest of this campaign."
Or at least until Saturday.
ABC News' Christine Byun and Kevin Chupka contributed to this report.