TOPEKA, Kan. (AP) — The top candidates for Kansas governor have big and radically different ideas for moving their state ahead, after its name became shorthand for failed tax policies.

Democrat Laura Kelly, a veteran state senator from Topeka, considers the state on the mend and has a list of places to bolster spending — while promising not to raise taxes. Republican Kris Kobach, the Kansas secretary of state and ally of President Donald Trump, argues that Kansas must return to cutting taxes to prosper.

But even with a past Republican tax-cutting experiment now rolled back and better-than-expected revenues, Kansas might not have much wiggle room for new spending. Even a relatively modest tax cut could force tough budget decisions to avoid shortfalls within the next five years.

Both candidates discuss their plans in broad terms, leaving many details for later.

Kobach is promising to shrink government, and Kelly is running as the fix for a mess left by eight years of GOP rule. In campaign stops and debates, neither has argued for having the state stand still for a while.

"That doesn't get anybody excited to vote," said state Rep. Steven Johnson, a moderate Republican from central Kansas involved in budget and tax debates. He adds that change is "a great message" but "the rubber meets the road when you tell me exactly how you're going to do it."

Kobach and Kelly have been in a dead heat for weeks. Independent candidate Greg Orman, a Kansas City-area businessman, has described them both as politically extreme but trails far behind.

A budget profile this summer from legislative researchers raises questions about how much new spending the state can afford. It shows that funding existing commitments could create a budget shortfall by 2023. While tax collections have been stronger than anticipated, additional school funding Kelly supports would eat up most of the surplus.

Critics argue that Kelly's spending priorities inevitably add up to tax increases. The Democratic nominee is undaunted — she also wants to cut the sales tax on groceries — and avoids specific numbers about spending.

"First and foremost we have to do the schools," she said after a recent campaign event. "Then we're just going to set up a list of priorities, and as the budget stabilizes and the economy starts to grow again, we will increase revenues coming in, and they will be there."

The budget profile raising questions about new spending assumes state revenues grow an average of 2.9 percent during the next four years. Kelly argues that state investments and budget stability will fuel economic growth; Brownback predicted that tax cuts would spur growth, generating revenues to prevent budget sacrifices.

Kobach has one specific tax proposal, rewriting the state's income tax code so Kansas stops seeing a windfall from changes in federal tax laws in 2017. Legislative researchers' profile suggested the windfall would avoid a budget shortfall before 2024, absent changes in spending.

But Kobach has avoided specifics about other tax cuts, saying their scope will depend upon how much spending the state can trim. He promises to attack the "decades-old government ethic" of spending "every penny" in annual budgets.

He says he would allow state retirees' jobs to remain unfilled and deny services to immigrants living in the U.S. illegally, though that idea has been challenged as impractical unless immigrants flee the state.

Legislators also commissioned a 2016 efficiency study . The state has adopted only about half of its 100-plus proposals; Kobach said he'd pursue many of the others.

"The agencies would come to the Legislature and say, "Look, we were able to get by with less, so please give us less,'" Kobach said while walking in a recent small northeast Kansas town's parade, with Frank Sinatra's "My Way" playing from Kobach's now-signature Jeep with replica machine gun.

Kelly has made the state's nationally notorious experiment in slashing income taxes in 2012-13 under then-Republican Gov. Sam Brownback a key issue. She was a visible player in the successful bipartisan effort last year to reverse most of the tax cuts, which resulted in a big income-tax hike to bolster the budget.

She backed a law enacted this year to increase aid to public schools over five years to satisfy a Kansas Supreme Court order in an education funding lawsuit. She supports boosting it further to account for inflation — something the court also directed.

Kelly also said recently that state universities and the foster care system for abused and neglected children are still hurting and Kansas needs to expand services for the mentally ill.

Some Kelly supporters see bolstering spending as crucial after Brownback's tax-cutting experiment and the budget woes that followed.

"We have to spend money to see economic growth," said Emily Kondziola, a 21-year-old Bethel College student and Democrat. "Her policies will require larger amounts of spending than we're seeing now, but we've seen trying to hold back the budget."

Still, many voters in Republican-leaning Kansas like Kobach's smaller-government message. John Mathews, a 40-year-old grant coordinator and Republican from the liberal bastion of Lawrence, said sales and income taxes are too high. He volunteered for Kobach's campaign.

He said, "Taxes are the main issue."

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Follow John Hanna on Twitter: https://twitter.com/apjdhanna .