Kansas Gov. Sam Brownback speaks during a campaign rally at New Steel and Pipe Supply in New Century, Kan., on Oct. 27. Polls show him in a tight race because many Republicans have defected in the wake of massive tax and spending cuts. (Colin E. Braley/AP)

Sam Brownback is hardly the only incumbent Republican governor struggling to hold his job in the waning days of Campaign 2014. But he holds one clear distinction over the others: He is at risk of becoming an object lesson in the limits of conservative governance in a conservative state.

Polls show the incumbent in a tight race against Democrat Paul Davis, the state House minority leader. It is close because many Republicans have defected from Brownback in the wake of massive tax and spending cuts.

If Brownback can bring home those wavering Republicans, he can win a second term — but so far he has not been able to do so. National Republicans worry that time is growing short.

The Republican Governors Association has dumped $4.9 million into Kansas, something that was not in its strategy book at the start of the 2014 cycle. New Jersey Gov. Chris Christie, the RGA chairman, recently put out a call to GOP governors and other surrogates to come to Kansas and remind Republicans of the gubernatorial race’s importance.

Meanwhile, Brownback is attempting a balancing act, distancing himself from many parts of his record while arguing that he will be proved correct in the end.

Democratic gubernatorial candidate Paul Davis, left, and incumbent Kansas Gov. Sam Brownback shake hands following a debate on Oct. 21. (Travis Heying/AP)

“We’re pushing hard,” Brownback told reporters here in a recent interview, referring to a final-days effort to rally the conservative base. He compared his tax and spending reductions to President Ronald Reagan’s tax cuts in 1981, which were followed by GOP losses in 1982 but then the “Morning in America” triumph in 1984.

“There was difficulty,” Brownback said of the immediate aftermath of Reagan’s cuts. “But it also then led to, I believe, 20 years of good growth in the country. Income tax policy does take time, but the data is all very clear about the impact of higher income taxes versus lower income taxes.”

The Kansas race has drawn national attention because of the high stakes involved, for Brownback and — with its potential policy implications — for the GOP. It also comes at the same time that Sen. Pat Roberts (R-Kan.) is facing his own tough reelection challenge, albeit for different reasons than Brownback.

If Brownback prevails, his victory will be seen as an endorsement of the Kansas experiment in supply-side economics. If he falls short, Republican governors in other states are likely to take his defeat as a warning about going too far to the right.

Brownback, who served 14 years in the Senate and ran unsuccessfully for president in 2008, is caught up in the latest chapter of a long-running conflict between Republican moderates and conservatives in Kansas.

For many of those years, the moderates prevailed, sometimes in concert with the Democrats. At times, the voters elected Democratic governors despite the state’s bright-red leanings overall. In the past four years, however, conservatives have gained the upper hand in the GOP and in the state — and with that has come a backlash.

That Brownback is in trouble might seem surprising, given that he won the governor’s office four years ago with 63 percent of the vote. He moved aggressively to implement one of the most conservative agendas of any governor in the country, patterned after Reagan’s supply-side policies. He signed off on deep tax cuts that he said would generate enough economic growth to turn the state around and also reverse the long decline in the state’s population.

Kansas Governor Sam Brownback, left, and Former Massachusetts Gov. Mitt Romney stump for Senator Pat Roberts (R-Kan.) on Oct. 27. (Julie Denesha/Getty Images)

So far, the program has not produced the predicted results, in growth rates or in state revenue. The state’s bond rating has taken a hit, and Brownback has been pilloried by critics over education spending.

Burdett Loomis, a political-science professor at the University of Kansas, said Brownback and his allies are paying a price for misunderstanding the 2010 election. “There was a fundamental misreading of 2010 as a great Kansas victory,” he said. “If you looked across the nation, it was a Republican sweep against Obamacare. He might have thought that the pendulum had swung farther than it actually had.”

Compounding Brownback’s problems was his decision to wade into a series of state Senate primary contests in 2012, siding with conservatives running against moderates. Nine moderate Republicans fell to conservative opponents in the GOP primary that year, cementing the conservatives’ hold on power.

“The place where it blew up was in the legislative races two years ago,” said a Republican who spoke on the condition of anonymity to offer a candid assessment of Brownback’s race. “Whether the governor did it personally or his people did it in his behalf, almost all the prominent moderates were defeated. That has really created political problems for him.”

Between the unhappiness over his policies and the intraparty conflict, Brownback suddenly became a vulnerable incumbent. Months ago, party leaders sensed his vulnerability but were confident he would prevail. Now there is genuine nervousness.

That Brownback is personally feeling the pressure was clear late last week when he spoke with a handful of reporters after making an announcement about a new state program designed to help stimulate growth in low-income urban neighborhoods. He sought to offer rebuttals to the attacks that have caused him the most trouble.

To the charge that he has cut education funding, he said that his opponent “is telling lies.” He argued that the state share of education spending has gone up each year, though overall education spending has not. There was a reduction in education spending his first year in office, he said, because the Obama administration’s stimulus money disappeared and the state could fill only part of that gap, because of a $500 million hole in the overall budget.

Critics also point to the fact that much of the additional state money has gone not to classrooms but rather into the pension system for teachers. Brownback said dealing with the pension system was a necessity. “Nobody’s going to work without a pension,” he said. “Our pension system was in the bankruptcy zone, and now it’s not.”

Chris Pumpelly, a spokesman for the Davis campaign, said in an e-mail that “Gov. Brownback is about the only one in the state who doesn’t know — or won’t admit — that there’s a serious problem with the way we’re underfunding our schools in Kansas.”

Asked how much he was hurt by involving himself in the effort to purge moderate Republicans from the state Senate, Brownback tried to play down his role. He blamed the courts for redrawing district boundaries and thereby throwing Republican moderates and conservatives into some of the same districts. He also said he got involved in only three of the battles. “I didn’t set this up,” he said. “The court redrew this map.”

Even on his tax cuts, Brownback offered a caveat to criticism of his program, saying he did not actually propose the income-tax rate cuts that he signed into law. “I proposed initially a flat tax with a small-business accelerator,” he said. “The legislature passed a rate cut. But you know, in these jobs, you get what they send you.”

When his economic program was implemented, however, Brownback described it as a “real, live experiment” in conservative economic governance. He is now pleading with Kansas voters to give him more time to prove that his program will work.

Brownback’s last-days push includes a controversial ad that began airing last week, criticizing the state Supreme Court for overturning the death sentences for two brothers convicted of multiple murders. It accuses Davis of supporting liberal judges. Davis told Brownback in a debate that it was “disgraceful” to attempt to exploit the tragedy of the murders.

Bob Beatty, a political-science professor at Washburn University in Topeka, said the Brownback-Davis race has outsize implications because it could answer whether Kansas remains a conservative state that prefers moderate governors or is one that wants to become a showcase for the rest of the nation for conservative ideas and policies.

“The stakes in that sense are unusual in politics,” Beatty said. “We often have races where people say it’s an important election. But in this case, you have to give Brownback credit for saying, ‘Here are the stakes.’ And his opponent is saying, ‘We understand, and we don’t like them.’ ”

Alice Crites contributed to this report.