"Those kinds of things where you can take it internally and say, 'Here's how I'm going to deal with this. Here's how I'm going to help this situation,' instead of going and protesting and saying, 'Oh, someone needs to pass a law to protect me'," Santorum went on.
CNN's Van Jones, who was part of the panel discussion, noted how his son was about to be high school age.
"I want him focused on algebra and other stuff," Jones argued. "If his main way to survive high school is learning CPR so when his friends get shot ... that to me, we've gone too far."
"I'm proud of these kids. I know you're proud of these kids too," Jones said to Santorum.
The former Pennsylvania senator agreed, but continued to make his point.
"I'm proud of them, but I think everyone should be responsible and deal with the problems that we have to confront in our lives. And ignoring those problems and saying they're not going to come to me and saying some phony gun law is gonna solve it," Santorum continued. "Phony gun laws don't solve these problems."
He also suggested that a much broader discussion about school safety was needed beyond all the talk of guns.
Santorum's comments immediately got noticed by Everytown for Gun Safety program manager Erica Lafferty, whose mother Dawn Lafferty Hochsprung had been the principal of Sandy Hook Elementary School, and died defending her kids.
"Rick Santorum's words are an insult to the kids of Parkland, my family and to the countless others who have had loved ones taken by gun violence," Lafferty said in a statement Sunday.
"My mother was killed while protecting her students at Sandy Hook School. For anyone to suggest that the solution to gun violence is for kids to learn CPR is outrageous, and indicative of the NRA's desire to do or say anything except strengthen America's weak gun laws," Lafferty said.
Santorum's comments also got the attention of Marjory Stoneman Douglas senior David Hogg, one of the most vocal students to survive the Parkland, Florida, Valentine's Day massacre.
It was Hogg and his classmates who organised Saturday's rallies.
"I think @RickSantorum might need to learn CPR for the NRA following midterms," Hogg tweeted Sunday afternoon.
Hogg and other Parkland, Florida student activists have called on Americans to vote out lawmakers not in support of stricter gun laws.
