"Having a gun and gun ownership is part of how people can feel safer," the former U.S. senator from Pennsylvania and 2012 GOP presidential candidate said during the roundtable discussion on on ABC's "This Week."
"I think we should stick to our guns," he said.
Former Michigan Gov. Jennifer Granholm, a Democrat, disagreed.
"This is not about taking people's guns away," she said. "It's about a narrow set of proposals that will enable use to enforce the existing the gun laws, the ban on assault weapons and a ban on high-capacity magazines."
Granholm cited popular support for the measures, and said the majority of citizens support the proposals.
Matthew Dowd, political strategist, said Obama is pushing the issue because he has been deeply affected by the Newtown, Conn., tragedy in which a young gunman killed 27 people, including his mother, before taking his own life.
He applauded Obama for discussing mental health, as well as having hospitals and professionals ask those at risk if they have guns in their homes.
But Santorum said the measures, if passed, won't decrease violence and mass shootings.
"Fifty years ago, you could go on a catalog and buy a gun. There were no restrictions on gun ownership," he said. "There were no restrictions on anything. And we had a lot less violence in society than we do today."