Gun control continued to be a hot-button topic on the Sunday political talk shows in the wake of the Connecticut school shooting.

California Senator Diane Feinstein proposed a new bill on Friday that calls for a ban on some assault rifles and semi-automatic weapons, as well as a ban on some high-capacity ammunition magazines.

Police Commissioner Ray Kelly and Rep. Paul Ryan of Wisconsin hit the Sunday political talk shows to weigh-in on the issue.

"Let's go beyond just this debate and we get deeper. What's our policy on mental illness? What's going on in our culture that produces this kind of thing?" Ryan said. "We need to have that kind of discussion and debate and I hope we don't skip past that and bring out political ideas that recycle failed policies of the past."

"The universal background check can be helpful," Kelly said on CBS' "Face The Nation." "About six million weapons estimated were sold last year without a background check."

The National Rifle Association says the new bill would infringe on the constitutional right to bear arms.