"I've spent five years of my administration working with my team to do a whole sort of things to try to reign in overdoses," he said.

"Sending kids mixed signals about drugs is a disaster," Kasich said at the third Republican debate.

Legalizing marijuana has become a rhetorical battlefield where "tough-on-drugs" GOP candidates like New Jersey Gov. Chris Christie and Carly Fiorina have faced off with libertarians like Sen. Rand Paul, who see it as an issue of states' rights.

"The bottom line is the states," Paul said at the previous Republican debate. "We say we like the 10th Amendment, until we start talking about this. And I think the federal government has gone too far. I think that the war on drugs has had a racial outcome and really has been something that has really damaged our inner cities."

While Paul called marijuana use a "victimless crime," Christie and Fiorina pointed to decreased productivity and negative impacts on family members as downsides to legalizing the drug.

An Oct. 21 Gallup poll found 58 percent of Americans support legalizing marijuana, according to a random phone sample of 1,015 adults. The issue of pot use is front and center in Colorado, the location of the CNBC GOP debate and one of four states where recreational marijuana use has been approved by voters. The others are Oregon, Washington and Alaska.

Watch our live coverage here or weigh in on the debate here.



— CNBC's John Harwood and Anita Balakrishnan contributed to this report.

