Since he's a member of the Senate, a more direct route than the judicial branch would be to pursue legislative-branch solutions, such as introducing a bill to amend the FISA statute in a more civil-liberties-friendly manner.
My original post was operating under the assumption that all branches would abide by the legitimate actions of the other branches. Grandparent is pointing out that sometimes this doesn't happen. Always a possibility, but not something I expect to see very often.
But, yes, I believe this is probably of a piece with his drone filibuster in terms of being political theatrics.
The judicial branch approach is meant to spur action and interest on the part of citizens. It's meant to create waves. He's intentionally looking to bypass the legislative branch because the outcome there is already known.
Not blaming the man, political capital is not free.
Of course, the Court is filled with know-nothings (as in, they are anti-abstraction, so there is no such thing as a valid governing principle, such as a right), so it's all probably pretty pointless.
Perhaps you're thinking of an alternate history where the Republicans were a primarily libertarian rather than a primarily conservative party?
But yeah, they're pretty libertarian with respect to the liberties they like. Everything else can go.