If WikiLeaks is prosecuted under the Espionage Act as it currently exists, then no journalistic institution or entity is safe. The idea that anytime that a journalist obtains a document that has "information related to the national defense" that could be used "to the injury of the United States" they could be subject to prosecution would destroy national-security journalism as it currently exists.
Also frightening is the reality that government officials looking to skew public debates one way or another regularly leak information to the press, so the government would really only be prosecuting people for publishing leaked information they didn't want leaked.
I think there's this idea that because the New York Times and the Washington Post are treasured journalistic institutions the government wouldn't dare engage in the kind of coercion it has leveled so effectively against Assange, and that even if he were prosecuted under an archaic unconstitutional law like the Espionage Act, he's a scary foreigner and there's no way that Americans would be treated the same way. But it really wasn't that long ago that Republicans like Bill Kristol and Rep. Peter King were talking about the NYT in the same kind of language they're using to describe Assange.
Sen. Joe Lieberman also called for Assange to be prosecuted, but he let slip that he thought other journalistic outlets could be held similarly "accountable," stating, "To me the New York Times has committed at least an act of, at best, bad citizenship, but whether they have committed a crime is a matter of discussion for the Justice Department."
Lieberman recently introduced the SHIELD Act along with Sen. Scott Brown, which would amend the Espionage Act to make it easier to prosecute Assange.