The closest the high court has come to ruling on this issue may have been the famous 1971 Pentagon Papers case, in which justices rejected a Nixon administration plea that they stop the New York Times and the Washington Post from printing a leaked top secret study of the history of US policy in Vietnam.
It was a landmark ruling in regards to US press freedoms. But what the ruling rejected was the government’s efforts to enjoin publication. A majority of justices appeared to indicate that it would have been possible for the administration to prosecute the two big US papers after they had printed the material. (Many of the judges weighed in with separate opinions, so it’s not entirely clear what they would have agreed upon in regards to this particular issue.)
If they do decide to bring a case, US prosecutors today would likely charge Assange or WikiLeaks with violations of the Espionage Act, a broad 1917 law.