Let's see.. have probable cause, obtain a warrant from a judge, then do your reasonable searches and the person has a right to an attorney...
This seems more like "well, spy on everybody, you never know who might be a suspect!" Which is what I'd expect a spy agency to do anyway, but it's ripe for abuse, what a bad precedent to set.
Spy on 300+ million people in order to catch a handfull of potential terrorists, and hey, nail all the people who disagree with you or you have something personal against in the bargain! :P