Asked whether he includes Paul -- a fellow potential 2016 presidential candidate -- in his criticism, Christie didn't back down.
"You can name any one of them that’s engaged in this," he said. “I want them to come to New Jersey and sit across from the widows and the orphans and have that conversation. ... I’m very nervous about the direction this is moving in.”
Christie acknowledged that there will always be mistakes when it comes to national security and protecting privacy, but said Americans need to stay focused on what's at stake.
He dismissed some of the current privacy/national security debates as "esoteric."
“I think what we as a country have to decide is: Do we have amnesia? Because I don’t," he said. "And I remember what we felt like on Sept. 12, 2001.”
In response, Paul's team said Christie doesn't understand what "esoteric" means and noted the growing ranks of those concerned about government overreach.
"Defending America and fighting terrorism is the concern of all Americans, especially Sen. Paul," Paul's former chief of staff, Doug Stafford, said. "But it can and must be done in keeping with our constitution and while protecting the freedoms that make America exceptional."
Paul himself also tweeted a response:
Christie went on to praise the national security strategies of both President Obama and George W. Bush.
“I want to say that I think both the way President Bush conducted himself and the way President Obama has conducted himself in the main on those types of decisions hasn’t been different because they were right and because we haven’t had another one of those attacks that cost thousands and thousands of lives," Christie said.
Christie appeared alongside Wisconsin Gov. Scott Walker (R), Louisiana Gov. Bobby Jindal (R) and Indiana Gov. Mike Pence (R). The four GOP governors appeared side-by-side at a session hosted by the nonpartisan Aspen Institute.
The four of them -- along with Paul -- are all considered among the GOP's top potential presidential candidates in 2016, with each of them ranking on The Fix's most recent list of the top 10 likeliest nominees.
The Republican Governors Association was holding its summer meeting in the mountainous resort town.
North Carolina Gov. Pat McCrory (R), who was slated to appear, had to stay in his home state with the state legislature moving on legislation -- including new abortion restrictions.
Updated at 11:59 a.m. Friday.