As a libertarian I'm inclined to believe that the whole idea of IP is just a farce made up by corporate interests. Maybe it wasn't like that in the beginning, but no doubt that's what it is today.
So, no, I don't think our apathy will allow the government to be overrun by copyright thugs -- we already have the cure and it's already prevalent.
Now, these are fairly base liberties being totally about the individual: "Copying data doesn't deprive. I want this data. Yay!" "Doing drugs doesn't hurt others. I want to feel different. Yay!"
The trick will be to maintain our loftier ideals like freedom of speech, freedom of press, and the right to privacy which I can very, very easily see being taken away.