The relevant liberty here is the liberty of data. It is probably the most widely exercised form of political protest/lawlessness/criminality today (drug use being a close runner-up: liberty of body).

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.