I recommend reading the whole thing, but the gist is that a federal video game bill proposed by Democratic senators Joe Lieberman, Evan Bayh, and Hillary Clinton — like similar state and local bills — is DOA because of the First Amendment.
Here are the relevant Supreme Court cases and lower court rulings striking down or granting preliminary injunctions against video game laws:
—Miller v. California (1973): The Supreme Court establishes a new standard for defining what constitutes obscene material. (Previous obscenity standards, which like Miller are concerned with sexual material, were defined in Memoirs v. Massachusetts  and Roth v. United States ).
—Ginsberg v. New York (1968): The Supreme Court establishes the concept of “variable obscenity” — something can be considered obscene for children (and therefore not protected under the First Amendment) even if it’s not obscene for adults.
—ESA v. Blagojevich (2005): Illinois’ Northern District Court strikes down two laws that made it a crime to sell or rent violent and sexually explicit games to minors. The decision delves deepest into the video game studies presented at trial and thoroughly shoots them down.
—ESA v. Granholm (2005): Michigan’s Eastern District Court grants a preliminary injunction against the part of a Michigan law that prohibited the dissemination of violent video games to minors. (The part of the law that prohibited the sale or rental of sexually explicit games was not challenged).
—VSDA v. Schwarzenegger (2005; last year was a busy one, thanks largely to Grand Theft Auto and Hot Coffee): California’s Northern District Court grants a preliminary injunction against a California law that prohibits the sale or rental of violent games to minors.
—VSDA v. Norm Maleng (2004): Washington’s Western District Court strikes down a Washington state law prohibiting the sale or rental of violent games to minors.
—IDSA v. St. Louis County (2003): U.S. Eighth Circuit Court of Appeals strikes down a Missouri county law prohibiting the sale or rental of violent games to minors.
–American Amusement Machine Association v. Teri Kendrick (2001): U.S. Seventh Circuit Court of Appeals grants a preliminary injunction against an Indianapolis ordinance restricting minors’ access to violent arcade games; the decision effectively overturned the ordinance. If you read any of these decisions, read this one by Judge Richard Posner. He goes beyond a narrow legal viewpoint to really grapple with the issue, and eloquently argues for video games’ relevance.
— March 19, 2006