The amendment led to a two-decade shift in state spending that saw higher education increasingly supported by the income tax, allowing lawmakers to use sales tax revenue for other public services.
But that shift has also diminished the funding available for Utah's elementary, middle and high schools, which are the lowest funded in the nation on a per-student basis.
Stephenson said he is looking at several reform options to address education funding, in part as a response to the Our Schools Now ballot initiative, which plans to ask voters in 2018 to approve a seven-eighths of 1 percent increase to Utah's income tax rate.
He described SB255 as a "shell," saying the higher education funding cap could be swapped out for other proposals based on the will of lawmakers.
"I hope that the committee will send the bill forward, even though this is not what I anticipate we will wind up with," Stephenson said.
Committee members were unwilling to take that leap, effectively directing Stephenson to try again before pushing the bill to the Senate floor.
Sen. Deidre Henderson, R-Spanish Fork, said that until the state's sales-tax base can be strengthened, capping the income-tax funds available for higher education would force lawmakers to choose between public services.
"This will have a detrimental impact either on higher education or on public safety," she said.
And Bridget Baldwin, a student from Utah State University, said limiting the money available for higher education would force students to bear the burden of increased costs.
"What this will end up doing is, probably, raising our tuition," she said.
Stephenson said he was willing to bring a new version of the bill back to the committee, likely one that would swap out the higher education funding cap with a five-year freeze of the statewide property tax that helps fund schools.
That rate currently adjusts down as property values increase, a revenue-neutral mechanism Stephenson was instrumental in creating.
But while local school districts are expected to raise taxes every few years to capture inflation, Stephenson said, the statewide property tax has lost "hundreds of millions" of dollars that would otherwise be supporting public education.
"There's been a lot of talk lately about freezing that rate," he said. "I believe now is the time to do that, at least for a five-year period."