There's more to this issue than Lieberman's bill. I recall recent discussion about re-defining the internet as a form of telecommunication like the telephone? So that the fed can regulate it, of course. Perhaps this is part of Lieberman's bill, I haven't read it.
Also, there is a recent move (May 2010) to have the FCC theoretically explore ways to stop 'hate speech' on the internet and in other forms of media. The internet looks to be their focus, as a few pages of google searches were attached to the petition to Congress. Unfortunately, the 'hate speech' targetted runs the gamut from true disgusting hate speech to so-called 'false arguments' and 'false facts', as perceived from the political perspective of the petitioners.
This petition reaks of control of the internet, along the lines of Chavez, who recently locked up some folks who posted opinions detrimental to Chavez. I'd rather see the internet shut down versus shut up.