Mathis said Thursday that the current rules on concealed weapons are confusing to the public and difficult for rural residents to abide by. Someone out horseback riding might have a gun and need to put a jacket on without worrying whether they need a permit to legally cover the gun.
"I think it brings clarity to the patchwork of laws about how you can carry guns," Mathis said. "This isn't about President [Barack] Obama or any federal issue or anything like that."
Utah law allows people to carry an unloaded weapon meaning a bullet is not in the firing chamber in the open.
In order to carry a concealed weapon, an individual has to take a class, pass a criminal background check and obtain a concealed-weapons permit.
If Mathis' bill passes, anyone over the age of 21 could carry a concealed weapon, unless they are specifically prohibited from doing so.
Opponents, like the League of Women Voters, say there is no reason to water down existing Utah gun laws.
"The league believes in well-regulated gun ownership to protect the safety of the community, and any attempt to roll back current laws about guns is an inappropriate move," said Jenn Gonnelly, co-legislative director for the league.
Herbert said it's too early for him to discuss whether he would veto the measure, but he appeared skeptical.
"I don't think there's really any big need to change what we have on the books," Herbert said.
Mathis, whose bill was approved by the House Judiciary Committee on Wednesday, said he was dismayed by the number of people in the audience who were openly carrying their firearms at the hearing, including some who were sporting semiautomatic rifles. He said it showed a lack for respect for others in attendance.
"I was really sickened by those people carrying in the open," Mathis said. "I don't think they understand what we're trying to do at all. We aren't trying to make a statement with this."