"It's a situation where you can carry a weapon without a permit, and it can be concealed or not concealed," she said.
The state issued 77,062 concealed weapons permits in 2012, according to Utah Department of Public Safety Firearms Supervisor Jason Chapman.
Chapman said close to 30 percent of those permits are for Utah residents the remainder were issued to out-of-state applicants. Utah's concealed-weapons permit is recognized in 33 states and is considered one of the most popular ones to obtain.
It runs $46 for Utah residents and $51 for out-of-state applicants.
Clark Aposhian, chairman of the Utah Shooting Sports Council, said his group is supportive of the proposal and said it was a "minor" change to state law.
"It doesn't have anything to do with [Newtown,] Connecticut, Columbine or Aurora," Aposhian said. "You still have to be lawfully in possession of the firearm. You can't be a felon. You're still subject to brandishing laws and not being under the influence of drugs and alcohol. And you can't go onto a school campus."
Utah is one of two states Kansas being the other where concealed weapons permit holders can lawfully carry on school campuses. The Mathis proposal wouldn't change that you'd still have to have a concealed-carry permit to be in possession of a firearm on a school campus.
House Minority Leader Jennifer Seelig, D-Salt Lake City, said her Democratic caucus hadn't had a chance to discuss the measure.
Mathis, a veterinarian in Vernal, did not return calls for comment.
But Seelig said her own initial concerns centered around legislation that was "fear-based" instead of looking to balance rights. She said guns would likely be the subject of a "robust" discussion when the session begins.
"Part of this discussion needs to involve the balancing of rights," she said. "Community rights, the rights of the individual to be safe and the right to bear arms is situationally contextual related to the forming of a militia."
The gun debate has heated up nationally in the wake of the Sandy Hook Elementary School Shooting that left 20 first-graders dead. President Barack Obama has asked Congress to institute an assault-weapons ban, reduce the size of magazines on firearms and tighten background checks.
On Saturday, about 1,500 people gathered at the Utah Capitol to rally on Gun Appreciation Day and Brian Greene, a newly elected Republican House member from Pleasant Grove, said he would carry a bill to allow local sheriffs to arrest federal agents attempting to seize guns from Utah residents.
Also, a strongly worded letter signed by the Utah Sheriffs' Association to the president said the elected county law enforcement officials were "prepared to trade our lives" in defense of the Second Amendment.
Salt Lake County Sheriff Jim Winder, the only sheriff in the state not a member of association, said he hadn't seen Mathis' bill and hadn't taken a position on it.
But he said the concealed-weapons permit process allows for people to learn if they're eligible to carry a firearm or not. He said people could be putting themselves at odds with the law by purchasing and carrying a gun without even knowing that they weren't eligible to do so. He also said it's helpful to officers who make a stop to know if a person is carrying a concealed weapon.
"It helps us to know that information so we don't have a misunderstanding or have any problems arise," Winder said.