The claim of executive privilege, made by the president to keep testimony or documents from compelled revelation, is not an absolute one. Thus, the claim must state the basis for its invocation. In US v. Nixon (1974), the Supreme Court decision that came just two weeks before, and arguably precipitated, President Nixon’s resignation from the presidency, the Court articulated the only three constitutionally permissible bases for the presidential claim of executive privilege.
The only bases for the invocation of the privilege are the need to protect secret deliberations and communications intended ultimately for the president that pertain to (a) military, or (b) diplomatic, or (c) sensitive national security matters. Just because two or more people in the White House discussed a matter or reviewed documents does not clothe their discussion or their document review with executive privilege. The conversation or document review must be integral to advising the president on his official duties, and it must fit into one or more of (a) or (b) or (c) above.
The invocation of the privilege can only be made by the president himself. Thus, President Obama will need to articulate and explain into which category--(a) or (b) or (c) above--his claim of privilege falls, and he will need to do so personally, either in person or in writing. The mere request by the attorney general for the president to invoke the privilege does not lawfully invoke it. As of this writing, the president has not yet done this.
When the president invokes the privilege, it is to prevent himself or others in the White House from being compelled to testify or to produce documents before a court or before the Congress. Since only the president can invoke the privilege, he must be aware of the subject matter addressed in the subpoenaed documents and he must know that the subject matter was discussed or the subpoenaed documents were reviewed as part of the process of advising him on running the Executive Branch.
It is unheard of for Department of Justice (DoJ) officials to bring documents in an on-going criminal investigation to the White House, and discuss them there. It is equally unheard of for White House advisors to go to the DoJ and discuss documents pertaining to an on-going criminal investigation there. We know that the documents in question pertain to an on-going criminal investigation because Attorney General Holder has repeatedly so stated in sworn testimony.
Under the Federal Rules of Criminal Procedure, DoJ documents involved in an on-going criminal investigation can only lawfully be discussed or reviewed--at the White House or at the DoJ or anywhere else--with persons lawfully involved in the criminal investigation or the administration of the criminal justice system. That leaves very few human beings outside the DoJ and inside the White House with whom Attorney General Holder or his DoJ colleagues may have lawfully discussed these documents. Certainly the president himself would be in this category.