I have no idea.
Whereas Bradley Manning is allegedly responsible for delivering stolen classified documents to Wikileaks and can be charged with espionage and breach of the Uniform Code of Military Justice, it’s difficult to see how Assange himself could be charged under US law for publishing those documents.
In New York Times v United States, the issue was whether the Nixon White House’s attempt to block publication of the Pentagon Papers was a violation of the First Amendment. (You can listen to the oral arguments here).
In that case, the test, which Justice Brennan formulated, was whether publication would cause an “inevitable, direct, and immediate event imperiling the safety of American forces”. If not, prior restraint was unjustified.
As long as Assange is a mere publisher of truthful and newsworthy content, and if the US cannot show a conclusive link to the above test being satisfied, in my view, he’s absolutely protected by the First Amendment – both in Civil and Criminal law.
Wikileaks published the bulk of its material by November 2010. If the Department of Justice was going to pursue Assange, I believe they would have done so by now.
The DoJ is interested in Manning, not Assange.
UPDATE 23 June
As Peter Galbraith writes in his Comment is Free piece of 21 June:
While the volume of material WikiLeaks released is staggering – millions of pages of classified State Department cables – it contains no intelligence reporting, and very little of what is truly sensitive. (Full disclosure: cables I wrote as ambassador to Croatia were among those leaked.) Ambassadors generally use special channels for policy recommendations, discussion of intelligence activities and for accounts of sensitive meetings with top officials. Private Bradley Manning had no access to cables in these channels, nor to intelligence reporting.
Even if Assange published intelligence – it still wouldn’t meet the NYT v US test unless it was tantamount to publishing upcoming troop movements in battle operations.