From the decision of District Judge Hon. Anna Diggs Taylor:
The Presidential Oath of Office is set forth in the Constitution and requires him to swear or affirm that he "will, to the best of my ability, preserve, protect and defend the Constitution of the United States."
The Government appears to argue here that, pursuant to the penumbra of Constitutional language in Article II, and particularly because the President is designated Commander in Chief of the Army and Navy, he has been granted the inherent power to violate not only the laws of the Congress but the First and Fourth Amendments of the Constitution, itself.
We must first note that the Office of the Chief Executive has itself been created, with its powers, by the Constitution. There are no hereditary Kings in America and no powers not created by the Constitution. So all "inherent powers" must derive from that Constitution.
We have seen in Hamdi that the Fifth Amendment of the United States Constitution is fully applicable to the Executive branch's actions and therefore it can only follow that the First and Fourth Amendments must be applicable as well.
More analysis at rollingstone.com/politics.