The US Government sought an injunction preventing the New York Times from publishing parts of the Pentagon Papers. The case quickly got to the Supreme Court, which threw out the injunction 6-3. It was one of those rare decisions in which nine justices generated ten different opinions. One was a basic, unsigned opinion of the court throwing out the injunction with barely any reasoning because the majority could only agree on the result, not the process to get there.
Suffice it to say, this is a very complicated question. I'm inclined to believe that any attempts to prevent journalists from publishing additional documents like the ones now in question will be quashed. But it's not a sure thing.
Also the fact that he is a supporter of the IRA, both in his statements for the past 40 or so years, and also materially (back during the Troubles). How the hell does a guy like that end up as Committee Chairman for Homeland Security?