Laird v. Tatum definitely bares some insight as to what the EFF is up against, the case is one of countless others in which the Supreme Court has considered the "chilling effect" of various government policies on protected expression.

If you're interested in this concept, take a closer look at Wieman v. Updegraff (where the term "chilling effect" was first used), Socialist Workers Party v. Attorney General, a case very similar to Laird, and Meese v. Keene.

The following paper goes quite deep into the matter:

http://www.bc.edu/dam/files/schools/law/lawreviews/journals/...