SPRINGFIELD, ILL., SEPT. 27 -- Three of the forces shaping America's politics this year -- aversion to taxes, distrust of politicians and concern for the future of children -- collided here at noon Wednesday.

The collision came in an appearance at a business group luncheon where Neil Hartigan, the Democratic candidate for governor, and Jim Edgar, the Republican nominee, discussed how to finance the state's contribution to public education.

A day earlier Hartigan, the state attorney general, announced that he would oppose extending a two-year, 20 percent state income surtax adopted in 1989 to help improve Illinois' schools. Sounding more like a Republican than a traditional Democrat, Hartigan said his opponent's "only answer to education and everything else is to raise your taxes again." He promised to find savings elsewhere in the budget to provide more money for the schools.

Edgar dismissed Hartigan's promise. "It's easy to talk about cutting waste before the election," he said, "but that type of demagoguery is going to ruin education in Illinois and I'm not going to be part of it. . . . Let's have the courage to say we aren't going to be able to cut your taxes."

The debate here mirrors the controversy that has stalemated the budget summit in Washington. Parallels can be found in most of the other 35 gubernatorial battles around the country. Nowhere in America, it seems, does anyone really know how to finance government services when people are deeply skeptical about the way the politicians spend their money.

The odd twist in Illinois is that it is Democrat Hartigan who is making what he calls "the conservative argument" that he can pay for what the voters want -- better schools -- by squeezing out what Ronald Reagan used to call "waste, fraud and abuse." And it is Republican Edgar, a protege of retiring Gov. James R. Thompson (R), who has been skirting perilously close to emulating 1984 Democratic presidential nominee Walter F. Mondale's tactic of saying taxes cannot be avoided.

Illinois, a geographical and political crossroads, is typical of many states. Even as federal income tax rates were lowered in the 1980s, taxes here were boosted repeatedly, but the state still struggles to maintain public services. Hartigan likes to point out that Thompson raised taxes 25 times in his record 14-year tenure, often citing schools' needs as the reason; yet increases in state spending for schools lagged well behind the increases in revenue those higher taxes generated while the state's share of overall education financing actually declined from 48 to 38 percent. He calls it "a con game," but does not point out that the Democratic-controlled legislature shared the responsibility for these decisions.

Illinois has a flat 2.5 percent state income tax and in 1988 the per capita state income tax payment was $272. A 20 percent surtax would increase the payment by $54 per person to $326.

Edgar, who knows public disillusionment with Thompson's record is a threat to his chances in November, is trying to shift the issue from past tax increases to the credibility of Hartigan's promise that he can finance school improvements without the surtax. Experts in state government, like those who showed up for the luncheon forum here, share Edgar's skepticism about Hartigan's ability to cut $573 million from non-education programs, eliminate 2,500 middle-management jobs and slash administrative costs 10 percent, with most of the savings replacing the $383 million that would be lost in surtax revenues for the schools.

"I'm very dubious about it," said Jack Van Der Slik, director of the Legislative Study Center at Sangamon State University here. "It's all very formulistic."

Hartigan's decision put him at odds with Chicago Mayor Richard M. Daley and with key leaders of the minority community. James Compton, head of the Chicago Urban League and chairman of the city school board, said retaining the surtax is "absolutely essential for the public schools throughout the state. It's the No. 1 agenda item in this {gubernatorial} race."

But Edgar has his own coalition problems. An underfunded, anti-tax Republican won 33 percent of the GOP primary vote against him. In the "collar counties" around Chicago, where the protest vote was highest, some Republican committee members believe Edgar is cutting his own throat. "He just doesn't understand the tax revolt is real," one of them said this week. Such fears became more acute last month when Hartigan ads aimed at the Thompson-era tax increases lifted the Democrat into a virtual tie with early favorite Edgar.

Edgar is not oblivious to the danger, even though he claims his private polls show Hartigan's surge has ended and he remains in front. The day before the Hartigan news conference, Edgar toured suburban areas, arguing that scrapping the surtax would inevitably damage the schools and boost property taxes.

His media consultant, Don Sipple, had an ad ready to go on the air Tuesday evening underscoring that point. It played adjacent to television news programs, some of which took a notably skeptical view of the Hartigan plan. Channel 2 in Chicago, for example, used the phrase "having it both ways" both in audio and on the screen to describe Hartigan's plan to cut taxes yet provide more money to the schools.

That kind of commentary is vital to the basic GOP strategy of shifting the issue from taxes to personal trustworthiness. The "character issue," Edgar said, "is Hartigan's biggest problem."

In a role reversal as striking as their positions on taxes, Edgar seeks to focus on Hartigan the public suspicion of politicians that has been fed by the actions of some of his own allies. Republican media adviser Sipple said, "The cynicism in Illinois is more pronounced, because Thompson twice did what President Bush has now done" -- reversed a campaign promise not to raise taxes.

But Hartigan's advisers are firmly convinced the real issue in Illinois is not character, but taxes. Pollster Mike McKeon said, "I told Hartigan a year ago that taxes would be the key issue" and that education "isn't even on the board."

A Chicago Tribune poll taken late in August reported that 60 percent of all voters and 66 percent of the crucial ticket-splitters said they favor continuation of the surtax if it is used for education. But McKeon dismisses that as the "moralistic answer" people think they are supposed to give, and says his research shows that by a 2-to-1 ratio voters are less likely to support a candidate who favors retaining the tax.

"Edgar's defense," he said, "is that they don't trust Neil Hartigan. But if one guy is holding a gun to your head and the other says he won't shoot you, which would you choose?"

The pollster's advice is reflected in the candidate's performance. Talking straight into the camera, Hartigan said he didn't need polls to know he was on the right side of this issue. "Everywhere I've been," he said, "you {voters} have told me you're working two, three jobs, and you're still barely making it. And these guys still want to raise taxes! Are they crazy?"

Edgar insists he is not crazy. "I know it's a risk," he said, "but I want to be governor so I can govern -- not to preside over chaos."

The voters have five weeks to decide who is playing the "con game" and whose policies spell "chaos" in the schools.

Special correspondent Lauren Ina contributed to this report.