However, it still would require a final vote by the Senate before the legislative session ends at midnight Thursday. Senate Majority Leader Ralph Okerlund, R-Monroe, said the chamber wanted to "have some good discussion" on the measure before a final vote.
Rep. John Mathis, R-Vernal, introduced the controversial bill that would have Utah join about a half-dozen states dubbed "constitutional carry" states.
Senate sponsor Allen Christensen, R-North Ogden, said Tuesday "it strengthens the Second Amendment right to carry a firearm" and he took issue with those who said the state requires licensing for everything from driving to cosmetology.
"We've mentioned licensing in here driving a car, braiding hair," Christensen said. "Doing all these things ... aren't a constitutional right. They are not. Carrying a weapon, having a weapon in your possession, is."
The measure had been altered from its original version, which would have allowed a person to carry a firearm loaded and concealed without a permit. In its current form, the bill would allow a concealed weapon to have a full magazine but the chamber must be empty.
Sen. Karen Mayne, D-West Valley City, a gun owner who noted her duck-hunting expertise during testimony, said training is critical to owning a firearm. Currently, to obtain a concealed weapons permit, a person must take classroom instruction though there is no requirement for live-firing on a range.
"It's deadly," Mayne said. "And if you pick up something that is deadly, you'd better be skilled at it or leave it alone."
Monday, several groups delivered a letter to Herbert urging him to veto the bill if it came across his desk.
Herbert on Tuesday stopped short of saying he would veto the bill but reaffirmed his opposition to it.
"Well, I've made my position pretty clear about it. I've got some concerns. I think the laws we have on the books work very well in protecting our Second Amendment rights," Herbert said. "'If it ain't broke, don't fix it' comes to mind and I don't think, at least in Utah, it's broken."
Deputy chief of staff Ally Isom said the governor "prefers to see legislation that informs, rather than inflames, the discussion."
Sen. Lyle Hillyard, R-Logan, joined five Democrats in voting against the measure echoing Herbert's comments that the current process of permitting to carry concealed firearms was satisfactory to him.
The measure passed the House 51-18 on March 1 and if the preliminary vote in the Senate holds, it would be close to the 50 House votes and 20 Senate votes it needs to be veto-proof.
Other states that have laws on the books similar to the Mathis proposal include Vermont, Arizona, Wyoming and Montana.