The past two days have seen a spike in supporters for the bill. The governor's office said there have been 1,200 contacts with people asking him to sign the measure into law. By contrast, there have been 585 contacts from people or groups against it.
That's a contrast from the previous week, where 973 people contacted Herbert's office to ask him for a veto while 323 sought his signature on the bill.
Both sides have hit the issue hard since the legislative session ended March 14. Herbert has until April 3 to make his decision on bills.
The Catholic Church sent a letter signed by Utah Bishop John Wester Friday urging his veto.
The Utah Shooting Sports Council (USSC) is sending alerts daily to several different groups of supporters that are delivering a steady diet of reasons for it to be signed.
But USSC Chairman Clark Aposhian isn't sure it will be enough for a signature and he ranks this fight as one of the top struggles he's had over a gun bill dating back to the debates over guns in schools and banning guns in churches.
"I don't think [the governor] likes it. I don't even have to wonder he's told me," Aposhian said. "He thinks Utah's gun laws are fine the way they are and the USCC would disagree and would like to see this changed."
The measure, sponsored by Rep. John Mathis, R-Vernal, has been controversial since the beginning of the session. It would allow a person to carry an unloaded firearm concealed without obtaining a permit. Unloaded in Utah, however, does allow for a person to have a full magazine but the chamber must be empty.
Aposhian said the bill is "a tiny step legislatively but conceptually, it's very big."
It passed in the House of Representatives 51-18 and in the Senate 22-7. Both vote totals narrowly surpass the number needed for a veto override 50 in the House and 20 in the Senate. But no one can say if those votes would hold steady if the Legislature were to convene in an override session.
Utah Chiefs of Police President Terry Keefe who is also the police chief in Layton said he got about 40 police chiefs from around the state to send letters urging a veto.
But Keefe said they've backed off in the past few days on lobbying Herbert.
"I think he pretty much understands our position," Keefe said. "I think it could be counter-productive to pester the man for repeated calls on this."
Opponents of the bill say it could result in people carrying concealed firearms who, had they been subject to the background check required for a concealed-carry permit, would have been denied the right to carry a gun under a jacket or in a purse.
Supporters of the measure believe carrying a firearm concealed or not is a constitutional right protected under the Second Amendment. Mathis has said it is also a matter of convenience for ranchers and farmers who work out in the field and wish to put on a raincoat over a gun without finding themselves in violation of the law.
Herbert, however during the last night of the legislative session, said in an interview he was "concerned about policy decisions being made by anecdote."
Robert Gehrke contributed to this report.