“A lot of people made it about me,” said Mr. Brownback, a farm boy turned successful lawyer, state secretary of agriculture, member of Congress and the 46th governor of Kansas. “But it’s not about me,” he said. “It’s about Kansas. It’s about the future of this state.”

The outcome in Kansas was likely to send a signal to other red states pursuing similar tax philosophies about the risks and limits of the approach. Republicans control 24 other state capitals, and some have likewise pressed for tax reductions and limits on spending, though few have taken steps as bold or sustained as in Kansas.

Even before this week, Democrats in states like Nebraska and Iowa have held out the Kansas model as a cautionary tale for their own Republican-run states. “It is something that Iowans talk about, that they don’t want to find themselves in a situation like Kansas,” said State Senator Janet Petersen, a Democrat in Iowa, where business property taxes were reduced in 2013 and where Republicans took control of state government this year.

First elected governor of Kansas seven years ago by a wide margin, Mr. Brownback wasted no time steering the Republican Party on a hard-right turn. In his first term, he helped push out moderate Republicans from the Legislature. Under his leadership, Kansas loosened restrictions on guns, made it harder for women to get abortions and passed some of the strictest voting laws in the country.

Most famously, he instituted the largest income tax cuts in Kansas history, a move that he promised would act “like a shot of adrenaline in the heart of the Kansas economy.”

All along, Mr. Brownback has been steadfast in his insistence that the sweeping tax cuts he had championed were sound, smart policy that would fuel growth. Kansas began collecting hundreds of millions of dollars less in revenue each year. In 2014, Kansans paid $700 million less in state taxes than the previous fiscal year, a far steeper decline than projected.

Last fall, as the policy faltered, the moderate wing of the party roared back, ousting legislators from the far right.