New Jersey Gov. Chris Christie and Kentucky Sen. Rand Paul continued their liberty vs. security debate Wednesday on “The Laura Ingraham Show,” with Christie dismissing his rival as an “alarmist.”

It was a continuation of a sharp exchange between the two candidates during Tuesday’s Republican presidential debate broadcast on CNN.

“Sen. Paul is an alarmist, and he’s a desperate guy who last night was trying to make some news, and I think he fell short,” Christie said.

The debate over how much freedom Americans should surrender in exchange for security is as old as the republic, itself. Within the large Republican presidential field, perhaps no candidates better represent polar ends of that schism that Christie and Paul. They have frequently tangled and did so again during Tuesday’s night’s televised debate in Las Vegas.

During that debate, Paul told viewers that if they want World War III, Christie is their candidate. Ingraham asked Christie about Americans concerned over the prospects of getting bogged down in another Middle East war.

“That’s not what we’re going to do,” he said. “And the fact is that we already are in World War III. And that’s what they need to understand. That’s what Rand Paul doesn’t understand … This is the war for our generation.”

In a separate appearance on the radio program, Paul fired back.

“I’m very concerned about big government Republicans like Christie who show such poor judgment in their own home state, shut a bridge down just to get back at a political opponent,” he said, referring to a scandal that has dogged Christie. “But also what he said last night should scare Americans to death.”

Christie’s proposal to impose a “no-fly” zone in Syria would set the United States on a collision course with Russia and possible war, Paul said.

“We have had calmer and wiser heads, both Republicans and Democrats,” he said. “Reagan was not the cowboy they portrayed him to be. He actually was very reasoned and wise … Contrast that with a blustering Christie who says, ‘Yes, I’m going to tell the Russians they can’t fly,’ coincidentally, where they are already flying.”

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But Christie said imposing a “no-fly zone” in Syria is a key part of fighting Islamic extremism and would provide cover for civilians who are fleeing the civil war. He suggested that it would help stem the flow of refugees trying to get in the United States and other Western countries.

“Let Syrians stay in Syria,” he said.

Paul lined up with Christie on criticism of the Republican Establishment. He said national security hawks and fellow GOP presidential candidates Sen. Marco Rubio of Florida and Sen. Lindsey Graham of South Carolina pay insufficient attention to strengthening the homeland.

“If you want to talk about defending the country, you really have to start with border security,” Paul said. “If you’re not willing to defend the border, all that other stuff sort of falls away.”

Like Christie, Paul blasted the $1.15 trillion spending deal that House Speaker Paul Ryan, R-Wis., negotiated with Democrats. He said massive spending bills that lump all appropriations bills together are recipes for mischief. He gave one example from last year: The U.S. spent $43 million to build a gas station in Afghanistan for vehicles using natural gas.

“It’s capitulation after capitulation,” he said. “Planned Parenthood continues, but so do a host of wasteful spending programs … I would let all funding expire and then I would put the shoe on the other foot, and I would say to the Democrats, ‘You now need to get a majority.’”