From my understanding of this, the six strikes thing isn't a law, and the US government isn't actually involved at all. I could be wrong, but I'm pretty sure that only the RIAA, MPAA, and some ISPs. The only people that are actually tracking your internet usage because of this are the ISPs, aka the people that already have access to everything you do on the internet. So I really wouldn't try to argue that this is a case of the government trying to take away your privacy.
Anyway, I don't really have a problem with this, assuming it only affects people that actually pirate stuff. I've actually been in favor of a system that is able to easily punish a large amount of people who pirate, without the punishments being totally absurd. And this seems like it could end up being this kind of system. Of course, I'll admit that I don't actually know very much about it, so I could be very off here.
Now, if this starts affecting people who aren't pirating, then it will be a problem. If people are getting copyright strikes for perfectly legitimate activity, such as legal torrents, then that could be a serious issue. In fact, the possibility of this negatively impacting people who don't pirate is the primary reason that I don't really support this, although my opinion could certainly change.