Republican rivals Gov. Chris Christie of New Jersey and Sen. Rand Paul of Kentucky are escalating their feud over national security policy and liberty.

In comments at a forum of Republican governors in Aspen, Col. Thursday, Mr. Christie said the libertarian strain championed by Mr. Paul currently coursing through the veins of political parties — as evidenced by broad, although ultimately unsuccessful, lobbying in the House of Representatives against NSA surveillance programs this week — is dangerous.

“This strain of libertarianism that’s going through parties right now and making big headlines I think is a very dangerous thought,” Mr. Christie said Thursday in Aspen, Colo. on at a forum of Republican governors. “You can name any number of people and [Mr. Paul is] one of them.”

Mr. Christie, like Mr. Paul considered a possible 2016 presidential contender, criticized what he called “esoteric, intellectual debates” that Mr. Paul and fellow conservatives such as Sen. Mike Lee of Utah have been conducting over the constitutional limits on unreasonable search and seizure and warrantless government surveillance.

Mr. Paul fired back Friday morning on his official Senate Twitter feed, writing that the governor “worries about the dangers of freedom. I worry about the danger of losing that freedom. Spying without warrants is unconstitutional.”

A top aide to Mr. Paul immediately fired back, telling The Washington Times the senator’s opposition to government drone policies and surveillance programs are designed to “protect the freedoms that make America exceptional.”

“If Gov. Christie believe the constitutional rights and the privacy of all Americans are ‘esoteric,’ he either needs a new dictionary or he needs to talk to more Americans, because a great number of them are concerned about the dramatic overreach of our government in recent times,” Paul senior advisor Doug Stafford said.

“Defending America and fighting terrorism is the concern of all Americans, especially Senator Paul,” Mr. Stafford, who is Mr. Paul’s closest adviser, said. “But it can and must be done in keeping with our Constitution and while protecting the freedoms that make America exceptional.”

Mr. Christie, appearing with Louisiana Gov. Bobby Jindal, Indiana Gov. Mike Pence and Wisconsin Gov. Scott Walker, told the Aspen forum that critics like Mr. Paul should sit down and sit across from the families of 9/11 victims. He noted that the Obama administration has largely kept in place the security and surveillance programs set up under GOP predecessor President George W. Bush.

“President Obama has done nothing to change the policies of the Bush administration in the war on terrorism. And I mean practically nothing,” Mr. Christie said. “And you know why? Because they work.”

“I want them to come to New Jersey and sit across from the widows and the orphans and have that conversation,” Mr. Christie said. “And they won’t, because that’s a much tougher conversation to have.”

Former Reagan White House official Don Devine, a traditional conservative whose latest book — “America’s Way Back: Freedom, Tradition, Constitution” — Mr. Rand has cited extensively in recent speeches, compared Mr. Christie to former Utah GOP Gov. Jon Huntsman, an early dropout in the 2012 GOP nomination race.

“Coming from the one person most responsible for the re-election of Barack Obama, I think we can take what Christie said with a grain of salt,” Mr. Devine said. “He will be the Jon Huntsman of 2016 if he enters the Republican presidential nomination race.”

And Mr. Stafford employed a shot of irony in hitting back at Mr. Christie, quoting the lyrics of New Jersey favorite son Bruce Springsteen: “In the words of the governor’s favorite lyricist, ‘You know that flag flying over the courthouse? Means certain things are set in stone: Who we are, what we’ll do and what we won’t.’”