The Republican governor spoke to reporters a few days after 20 children and six adults at Sandy Hook Elementary School were slain by a gunman packing a high-powered rifle.
Haslam said he doesn't know if there will be any changes to gun laws in Tennessee, but he does expect heavier debate on a contentious measure that would give employees the right to store weapons in vehicles parked at work.
The business lobby opposes the measure backed by the National Rifle Association on the basis that it would intrude on their property rights. Gun advocates argue that banning guns in company lots effectively prevents workers from being armed during their commute.
Haslam said earlier this month that the exclusion of college campuses is key to the bill's passage in the upcoming session, and he reiterated that on Monday.
"I have expressed a particular concern with education institutions, and still feel that way," he said.
As for the state's mental health programs, Haslam said there's been a request for increased funding, and "that will be part of what we look at" this session.
At least one law enforcement official has said the 20-year-old Connecticut gunman, Adam Lanza, had been diagnosed with Asperger's, a mild form of autism often characterized by social awkwardness.
People with the disorder are often highly intelligent. While they can become frustrated more easily, there is no evidence of a link between Asperger's and violent behavior, experts say.
Authorities said Lanza decided to kill himself when he heard police closing in about 10 minutes into the attack.
Richard Novia, the school district's head of security until 2008, who also served as adviser for the high school technology club, of which Lanza was a member, said he clearly "had some disabilities." Novia now lives in Spring Hill, Tenn.
"If that boy would've burned himself, he would not have known it or felt it physically," Novia said in a phone interview. "It was my job to pay close attention to that."
Overall, Haslam said the massacre will spur debate for months to come.
"Your first response is being sick at your stomach," the governor said of first hearing about the shootings. "I was with people all weekend who kept coming back to that. I think it's something the American people are having a hard time getting past, and I hope we don't get past it fast."
Haslam said the Tennessee Department of Education is expected to host a discussion in the near future about security and safety in the state's schools.
Meanwhile, some state lawmakers were already tossing around ideas following the Connecticut tragedy.
Newly elected Republican state Sen. Frank Nicely of Strawberry Plains tweeted Monday that he plans to introduce legislation that would put armed school resource officers in just about all state schools.
"A lot of the middle schools have them; elementary schools don't have them," Nicely told The Associated Press. "What we're trying to do is have a resource officer, or let one of the current staff take some training to carry."