The bill was held after a lengthy debate Monday about the idea of holding gun owners civilly liable if they lend the weapon to someone who uses it in a crime.
Rep. Andrew Stoddard, D-Sandy, filed House Bill 190 after McCluskey was shot and killed at the U last year. The man who killed her borrowed the weapon.
"What I want to do is something specifically for gun owners because they should be held to a higher standard because their product is inherently different," he told reporters.
The House Judiciary Committee was divided on the subject.
"There are many reasons that the state of Utah and the University of Utah failed Lauren McCluskey," said committee chairwoman Karianne Lisonbee, R-Clearfield.
She said the bill went after "innocent gun owners," instead of the actual person committing a crime.
"I would encourage potential victims to arm themselves. To learn how to properly use a gun. And then, if they’re in danger, to use it," she said.
But Rep. Eric Hutchings, R-Kearns, said that while he had concerns with the bill, he believed gun owners should take some responsibility.
"Firearm owners have got to start owning this thing. They really do," he said.
Public comment was divided on the bill. The National Rifle Association and Utah Shooting Sports Council opposed it, while March for Our Lives Utah, the Gun Violence Prevention Center and YWCA of Utah supported it.
House Minority Leader Brian King tried to pass the bill out, but the committee overruled him. Rep. Stoddard planned to bring it back next year.
"I think anyone bringing a gun bill in Utah has a lot of work to do. They’re not easy to pass, but it’s a conversation that’s worth having," he said.