The United States government has done an excellent bit of propaganda to convince the bulk of the public that they are the most free people on earth. We salute the flag and sing the national anthem at games. We have the presidents' pictures on the walls of our classrooms. We chant "USA" at political rallies.
But the government of the United States has perpetrated terrible violence and destruction of liberty against its own citizens and many more abroad. Through endless military engagement abroad to harassment, detainment, and imprisonment at home, the government serves its own interests first, and enhancing and preserving your liberty is not among them.
I should be very concerned about coming to the attention of anyone within government -- at any level. Even the local code enforcement board can extract time, energy, and money from you should you come under scrutiny.
But as others have said, you're already on the lists. No need to be paranoid. Go ahead and sign the Snowden petition. It's just one more data point on your dossier. The government already has enough on you to put you away for life if you become inconvenient to the state. Three Felonies a Day[1] and all that.
[1]: https://www.amazon.com/Three-Felonies-Day-Target-Innocent/dp...