In this case, the New York Times got a hold of leaked and classified documents, called the "Pentagon Papers". The Nixon administration sued to prevent the publication of said documents. However, the First Amendment prevailed in the end, when the U.S. Supreme Court handed down a 6-3 verdict against the Government.
From the WikiPedia Article, the concurring opinions were as follows....
Justice Hugo Black wrote an opinion that elaborated on his view of the absolute superiority of the First Amendment. He was against any interference with freedom of expression and largely found the content and source of the documents to be immaterial. Justice William O. Douglas largely concurred with Black, arguing that the need for a free press as a check on government prevents any governmental restraint on the press.
Justice William J. Brennan, Jr. wrote separately to explain that the publication of the documents did not qualify as one of the three exceptions to the freedom of expression established in Near v. Minnesota (1931).
Justice Potter Stewart and Justice Byron R. White agreed that it is the responsibility of the Executive to ensure national security through the protection of its information. However, in areas of national defense and international affairs, the President of United States possesses great constitutional independence that is virtually unchecked by the Legislative and Judicial branch. "In absence of governmental checks and balances", per Justice Stewart, "the only effective restraint upon executive policy and power in [these two areas] may lie in an enlightened citizenry - in an informed and critical public opinion which alone can here protect the values of democratic government."
Justice Thurgood Marshall argued that the term "national security" was too broad to legitimize prior restraint, and also argued that it is not the Court’s job to create laws where the Congress had not spoken.