Host Bob Schieffer noted that the program could not get a Republican on the Senate Judiciary Committee, which Schumer sits on, to appear on the program. All either simply said "no" or that they were unavailable.
"Where do you see this going now?" Schieffer asked.
"Well, I think we could be at a tipping point for two reasons, a tipping point where we might actually get something done," Schumer said. "First, this was not a single incident. It followed a series of others in the last few months we've had mass shootings in Oregon and Wisconsin and Colorado. When the public sees these as isolated incidents, they're less upset than when they occur one after the other. And the public will not accept, the public will not accept as a new normal, one of these incidents every month, these mass shootings."
He also noted that the involvement of children in the recent shooting has made an especial impact on people's views on gun control.
With the caveat that no one yet knows what exactly might or might not have prevented the shooting at Sandy Hook Elementary school, he argued that three major changes in gun control policy could prevent more mass shootings.
"One is to ban assault weapons, try and reinstate the assault weapons ban. The second is to limit the size of clips, to maybe no more than 10 bullets per clip. And the third would be to make it harder for mentally unstable people to get guns," he said.
He noted that Jared Loughner, who killed six people in January 2011 when he opened fire on a crowd where former Arizona Rep. Gabrielle Giffords (D) was meeting with constituents, was tackled when he paused to reload.
Schieffer asked Schumer why it was so difficult to not only get gun control laws passed but to even start a discussion on the topic. "I think they're more reluctant to talk about this than they are about raising taxes," Schieffer said of the GOP.
Schumer mentioned the general "gridlock" between parties.
He also said as author of multiple gun control measures, he has spent "more of my time trying to stop bad things from happening than being able to to good things."
But he also noted, "Those of us who are pro-gun control have to admit that there is a second amendment right to bear arms. I know that my colleagues on the pro-gun side say, 'How can the liberals, how can the left say the first, third, fourth, fifth, six amendments should be read expansively, and the second amendment should be seen so narrowly through the pinhole of, well, it's only malicious.'"
He said that the right would potentially be "more wiling to admit" that no amendment is absolute if those on the left felt more comfortable discussing the constitutional right to bear arms.
"The first amendment has limitations. You can't scream fire in a, falsely scream fire in a crowded theater," he said, as well as laws regarding libel and pornography."
"If together we can come to the middle on that," progress is possible, Schumer said.
Watch the video, via CBS, below.
