One factor is that Jewish groups fear government remedies for violence in the popular media are likely to be ineffective and may have constitutionally catastrophic side effects. The issue has been largely monopolized by religious right leaders who seem more eager to use it to discredit liberalism than to find solutions. Many of the Christian crusaders, Jews fear, want to censor a broad range of ideas not to their liking, not just images of violence. Today, it's bloody video games, but tomorrow it may be non-Christian ideas. And Jewish groups tend to see the problem of children's access to objectionable materials as a matter for families, not governments.
Jewish groups worry about the broader implications of that desire.
There's also uncertainty over the issue of Jewish involvement in the entertainment industry. Cumulatively, these factors have put Jewish leaders in a bind. They recognize that the cultural factors work together with the flood of guns to produce horrific violence. But in their public activism they feel most comfortable focusing on the gun part of the equation. But in doing so, they forfeit the game to those who will not be nearly as respectful of the First Amendment.