There was a huge discussion about this exact thing a month or two ago on another message board I go to.
The best argument people like Leiberman can muster is that "Studies show that when you let a five year old watch violent movies or play violent video games, they immediately begin to act more aggressive and hostile." Yea well, that's great argument in theory, IF WE WERE ALL FIVE YEARS OLD. The only way they could possibly have a point would be to follow several people (hundreds, if not thousands) for their entire lives, and see which ones develop violent tendencies dependent on which media they are exposed to. You'd have to monitor so many different factors - environment, which games are played, family history, any possibly psychological illnesses...etc etc etc, the list goes on and on. In the end, you're left with a bunch of scattered facts and generalizations that ultimately prove nothing.
Yea, I wouldn't be surprised if a kid played GTA, Mortal Kombat, Postal, etc., all his life, if he wouldn't become desensitized to violence. But MAKE him violent? That's a completely different tangent.
Using non-sequiter logic, however, is every politician's ace in the hole, so I'm not surprised to see the same argument being utilized over and over.