Tomorrow’s vote on a Utah ballot referendum is shaping up as the next test in the campaign for school vouchers.

Voters will determine whether Utah becomes the first state in the nation to enact a universal school voucher program, letting any parent in the state use a voucher to pay for private school. Limited voucher programs are already in place in Cleveland, Milwaukee, and the District of Columbia, and voucher advocates hope that a victory in Utah could give the policy initiative new momentum.

Fueled by more than $8 million in campaign spending, one and a half times what was spent in the last governor’s race in Utah, public discussion on what is known as Referendum One is vigorous. Several people said it is impossible to set foot in the state without noticing the bright signs in yards and windows begging citizens to vote yes or no, or being bombarded by television and radio ads filling the airwaves.

Even the Utah Jazz basketball game Saturday night was the scene for a showdown, as voucher supporters sandwiched between yellow “Vote For 1” signs received reactions that a leading advocate of vouchers, Patrick Byrne, said ranged from cheers to spitting on his shoes.

Mr. Byrne, the CEO of the Salt Lake City-based company Overstock.com, has poured more than $4 million of his personal fortune into supporting the voucher push, matching more than $3 million in anti-voucher spending by the nation’s largest teachers union, the National Education Association.

Mr. Byrne said the fight is attracting so much attention because it could be a prelude to a cascade of similar programs across the country. “Why is the NEA here? Because they understand the national implications,” he said. “They understand that this is the ice-breaking, and if it gets in and it succeeds, it would have a demonstration effect.”

Teachers unions strongly oppose school voucher programs, arguing that they weaken public schools. But the programs have been making steady progress across America despite the opposition, with city-based programs cropping up in Milwaukee, Cleveland, and the District of Columbia.

If okayed by voters, the program passed by the Utah state legislature in February would be the first publicly funded universal statewide voucher program. A program in Florida that offered vouchers only to students enrolled in failing public schools was struck down last year by the state’s supreme court. Any Utah child now in public school — and any child in the state not yet of kindergarten age — could receive a voucher for use at a private school in lieu of public schooling. Depending on a family’s income, vouchers would range from $500 to $3,000.

The latest polls suggest a yes vote is unlikely, with a 20-point spread between opposition to the measure, 56%, and support, 36%. Only 8% of voters told the Salt Lake Tribune they were undecided. Arguing his cause is still alive, Mr. Byrne, who holds a philosophy Ph.D. from Stanford, where he met his mentor, the late voucher supporter Milton Friedman, quoted Beowulf: “Fate often saves the undoomed warrior if his courage endures.”

“In other words,” he said, “it may all look hopeless, but if you don’t throw in the towel and you keep fighting, once in while the gods come in and do you a favor. I am hoping for a favor from the gods.”

Mr. Byrne said he supports private school vouchers because he believes that the government should not have a monopoly on education, which he called “the only domestic issue that really matters.” He said the idea to bring vouchers to Utah has been eight years in the works, and he said he discussed it with Friedman before his death, who called the plan “half a loaf” next to his ideal, because it still has government interventions and regulations. But he said Friedman supported the effort anyway as an important first step.

Opponents of vouchers are painting the vouchers push as a corporate man’s lone mission for privatization, but Mr. Byrne said the coalition behind him is large and diverse, with a mix of Republican males and black and Hispanic minority groups of both sexes. A group of prominent business leaders in the state have reportedly been urging their employees to support the referendum, and a Hispanic group recently launched a campaign in support of vouchers.

Labor groups lead the opposite coalition, Utahns for Public Schools, which is headquartered in the same building as the leading teachers union and which has received 97% of its funding from union groups and individual union members. A spokeswoman, Lisa Johnson, said support is also coming from the state parent-teacher association, the National School Boards Association, the NAACP, La Raza, the League of Women Voters, and a disability rights group.

Ms. Johnson said vouchers would divert money from public schools, which already receive less money for each student in state funds than any state in the country. She said the modest size of a voucher would distort who uses the program, with poor families unable to afford the extra $5,000 a year it would cost to pay the average private school tuition in the state, $8,000.

The president of the American Federation of Teachers local in Utah, the state’s smaller teachers union, Deborah White, said she is also pitching in to fight the referendum, corralling the power of thousands of AFL-CIO members to pitch in for tomorrow’s get-out-the-vote effort.

“Union members understand the idea of privatization,” Ms. White said. “When you start to privatize anything, you lose the control of quality, such as highly qualified educators and how the money is spent.”