On April 29 Thom refered to the General who ran the NSA having said that they follow the fourth Amendment.
The Fourth Amdt starts out :"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures shall not be violated, ..." The first test is: does the search involve "their person, houses, papers, and effects." I'm sure that the NSA lawyers will tell you they do not search persons, houses, papers or effects. Their job is searching the radio waves and digital information in the air - so they do not have to obtain a warrant, they do not have to show probable cause, write any sworn affidavit, or describe places to be searched or persons or things to be seized.
If the NSA was a state agency in Washington State they could not do this because the Washington Constitution states the people shall be secure in their "personal affairs." The Washington Supreme Court has decieded that "personal affairs" means almost anything that can be connected to an individual including radio waves and digital information from space.