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The debate promises to test the enduring relevance of one of the most fundamental principles of modern conservatism supply side economics, the idea that if you cut taxes far enough, the economy will expand to the point that it generates new tax revenue.

With the federal deficit growing and economic growth sputtering along in the low single digits, the Republican Party is facing questions from within over what many see as a blind faith in the theory that deep tax cuts are the shot of economic adrenaline a languid economy needs.

Tax cuts good. And thats about as much thinking that goes into it, said Chris Buskirk, a radio host and publisher of American Greatness, a conservative online journal. Now, he said, Republicans in Washington seem to be in an arms race to the lowest rates possible.

Everybody is trying to overbid each other, Mr. Buskirk said. How much more can we cut?

Outside Washington, Republicans are discovering there are limits.

In South Carolina, Republicans overrode their governors veto and a blocked a filibuster to increase the gas tax. They also rejected a series of broader tax cuts on the grounds that they were too expensive and voted instead to create a smaller tax incentive for low-income families.

The Republican governor of Tennessee, Bill Haslam, signed into law the first increase in the states gas tax in almost three decades. He defied conservative groups that said a state with a $1.1 billion budget surplus had no business asking people to hand over more of their money.

And in the most striking rebuke of conservative tax policy in recent memory, Republicans in Kansas have undone much of the tax overhaul that Gov. Sam Brownback held up as a model for other states and the federal government to emulate.

A fantastic way to go, he said this year, urging Mr. Trump and Congress to follow suit with deep reductions to corporate and individual rates. But Republican lawmakers in Kansas decided that they could cut only so much without doing irreparable harm to vital services and voted to increase taxes by $1.2 billion last month. Mr. Brownback vetoed the plan, but Republicans overrode him.

Much of the devotion to tax cuts as an inviolable Republican principle stems from the success that President Ronald Reagan and Congress had in 1981 when they agreed to an economic recovery package that included a rate cut of about 25 percent for individuals.

But at that time, the highest marginal tax rates approached 70 percent, leaving much more to cut and a much larger chunk of money to be injected back into the economy. At some point, economists said, tax policy that is too aggressive leaves too little money to inject to make a difference.

Bruce Bartlett, who advised Reagan on the 1981 tax cuts, chastised Republicans for what he described as their reflexive desire to drive rates lower.

The essence of what the supply-siders were trying to accomplish was accomplished by the end of the Reagan administration, Mr. Bartlett said.

Yet, he added, Republican policy still mimics what was done under Reagan. Theyve got to keep pressing ahead no matter what, he said.

The situation in Kansas was, for at least some conservatives, a jolting realization that tax cuts can be too blunt an economic instrument.

After Mr. Brownback took office in 2011, he pursued a plan that included cuts and, in some cases, an outright elimination of taxes for businesses and individuals to help invigorate the states underperforming economy. He described it as an experiment in conservative governance that could demonstrate what Republicans were capable of if they controlled legislative and executive branches across the country. (He is Kansas first Republican governor since 2003.)

The conservative movement got behind him. The plan was approved with the lobbying muscle of the billionaire Koch brothers political network, which is overseen from Wichita, where one of the brothers, Charles G. Koch lives. It had the blessing of prominent conservative economists like Stephen Moore and Arthur Laffer, the Republican Partys foremost supply-side evangelist.

In urging the Kansas Legislature to act, Mr. Laffer and Mr. Moore said the cuts would have a near immediate positive impact on the economy. Mr. Brownback said the plan would pay for itself.

That is where the parallels with Washington start to trouble those who are critical of the plan the Trump administration has laid out. The plan would slash the rate paid by businesses to 15 percent and shrink the number of individual income tax brackets from seven to three 10, 25 and 35 percent.

Mr. Laffer and Mr. Moore, a Heritage Foundation economist, have both helped shape the presidents tax policy.

Steven T. Mnuchin, the Treasury secretary, said the Trump tax cuts would pay for themselves with the economic growth they would inevitably create.

In Kansas, the predicted economic bloom did not materialize. Employment and economic growth have lagged far behind the rest of the nation. The state treasury had so little money to spread around that the Kansas Supreme Court found that the states spending on public education was unconstitutionally low.

If there were three words I could say to Congress right now, said Stephanie Clayton, a Republican state representative from a district in the Kansas City area, they would be, Dont do it.

She criticized what she said was a desire by her party to be more faithful to the principle than to the people Republicans were elected to help. Mr. Brownback and many conservatives, she said, overpromised on the tax cuts as a sort-of Ayn Rand utopia, a red-state model, citing the author whose works have influenced the American libertarian movement.

And I loved Ayn Rand when I was 18 before I had children and figured out how the world really works, Ms. Clayton added. Thats not how it works, as it turns out.

Mr. Trump and Republicans in Washington are undeterred. Kansas, they argue, is not an economic microcosm for the country, with its unique dependence on energy, agriculture and aircraft manufacturing. And lawmakers there never could reduce spending enough to correspond to the much lower level of tax revenue coming into the state treasury.

Many conservatives who support a tax overhaul said they anticipated considerable growth with a reduction in corporate rates, which are among the highest in the world. If those are lowered to 15 percent, down from the current 35 percent, businesses will not only reinvest in the United States but relocate here, they said.

At 15 percent, Swiss bankers will move here, said Grover Norquist, president of Americans for Tax Reform.

But restraining federal spending is still going to be a key part of the equation. What you need is not an explosion of spending, Mr. Norquist added. And you need the economy to grow faster than the size of the government.

In a world in which Mr. Trumps deconstruction of the administrative state reduces the size and cost of the government, the tax cuts make sense. But if lawmakers do not have the nerve to find savings somewhere, like in the social safety net for retirees, the outcome could end up resembling something close to Kansas failed experiment.

The question is whether you can put together some kind of revenue-neutral tax reform, said N. Gregory Mankiw, a professor of economics at Harvard and chairman of the Council of Economic Advisers under President George W. Bush. I dont see the political will to do that right now. Certainly not in this environment.

A version of this article appears in print on July 3, 2017, on Page A10 of the New York edition with the headline: Cut Taxes? In States, G.O.P. Goes Other Way.

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