CORALVILLE, Iowa — Election seasons in this small eastern Iowa town are usually cordial affairs. But this year, a group backed by the billionaire Koch brothers has changed that.

The group, Americans for Prosperity, has jumped into the race to elect Coralville’s next mayor and City Council with an aggressive campaign, mailing fliers, advertising in newspapers, calling voters and knocking on their doors. Its latest leaflet hit mailboxes last week, denouncing the town’s growing debt and comparing it to the financial woes of Detroit. “Coralville is fast becoming Iowa’s version of Detroit,” it read.

Tuesday’s race here is not the only one that has drawn the interest of Americans for Prosperity, which was founded by Charles and David Koch. Local chapters have been involved in property tax fights in Kansas, Ohio and Texas, the group says.

In January, the group successfully fought an increase in a food and beverage tax in Fremont, Neb. And last spring, it opposed a tax increase in Gahanna, in central Ohio. Voters rejected the tax measure in May, but the City Council has put it back on Tuesday’s ballot.

Tim Phillips, the national president of Americans for Prosperity, said the organization could have a real effect on local races, where it does not have to deal with all the Washington special interests.

The main reason “we fight local issue battles is because they result in good policy outcomes, generally promoting economic freedom via less taxes, less government spending,” he said.

But here, in this town of fewer than 20,000 residents, the group has not been so welcome, and the nonpartisan campaign has become an informal referendum on the involvement of outsiders.

Even residents who agree with Americans for Prosperity’s core argument — that the city’s debt is out of control — question the group’s motives for wading into the race. That has forced the candidates who share the group’s beliefs to keep the organization at a distance.

Chris Turner, a first-time candidate for the City Council who has spoken out against the debt, said that although he disagreed with Americans for Prosperity on most issues, he could not seem to catch a break because his campaign platform aligns with the organization.

“Every time I go to a debate or anything, I’ve tried talking about the budget, and then they just go, ‘Koch brothers, Koch brothers, Koch brothers,’ ” he said of his critics, adding that he wished Americans for Prosperity “would just go away.”

The organization’s Iowa chapter, one of 35 affiliates across the country, is running the campaign in Coralville. Mark J. Lucas, the president of the Iowa chapter, lives in Iowa City, a college town that neighbors Coralville. He said he took an interest in the Coralville race because the city’s debt and its economic development strategy affect taxpayers across the state who have to make up Coralville’s shortfalls.

Americans for Prosperity is not openly promoting specific candidates, and Mr. Lucas would not say how much money it is spending.

“For me as a state director, I’m the one who picks the strategy,” said Mr. Lucas, a native Iowan. “It’s not, like some people think, the Koch brothers are telling us, ‘You need to play in the Coralville City Council race.’ That’s absolutely not true.”

But David Jacoby, a Democratic state representative from Coralville, questions the motives for Americans for Prosperity’s involvement in a local race in which eight people are running for three council seats and four people for mayor.

“I think right now, too, that they’re doing whatever groundwork they can for the 2014 elections — so any inroads they can make anywhere,” Mr. Jacoby said.

Americans for Prosperity seems to be winning few adherents here, or at least anyone willing to admit so publicly. After all, eastern Iowa was a Democratic stronghold in 2008 and 2012, when the state went for President Obama. Thumbing through a survey at Kathyl Jogerst’s door on a rainy afternoon last week, John Sevier, a 22-year-old volunteer with Americans for Prosperity, started a question to her by saying the City Council had moved $5 million out of the school district budget.

Ms. Jogerst, 61, cut him off.

“No, they didn’t,” she said with a skeptical chuckle.

“Are you sure?” Mr. Sevier said.

“Yeah, yeah,” she said, quickly explaining her position without allowing him to get a word in. “I know the agenda with your group.”

One of the central players in the race, a coalition of business leaders called Citizens for Responsible Growth and Taxation, has a large disclaimer on its website that says it is unaffiliated with Americans for Prosperity.