I am somewhat skeptical that either the ACLU or EFF are effective organizations for this cause. The ACLU in particular have drifted significantly from a civil liberties focus, and EFF's privacy track-record for corporate run surveillance has never been the best and of late they seem to be following the ACLU away from civil liberties.

There is an increasingly popular idea that all libertarianism, including civil libertianism, is inherently partisan and specifically right-wing. I think it has done a lot of damage to these organizations' ability to effectively fight this and other issues. I've shifted a lot of my support for ACLU/EFF towards IJ in recent years.