Arkansas is not a battleground in the presidential race, being solidly in Mitt Romney’s camp. It doesn’t have a U.S. Senate contest or gubernatorial election this year. Even its four House races are not considered competitive.

But Americans for Prosperity (AFP), a conservative group backed by billionaire brothers Charles and David Koch, has pledged to spend nearly $1 million here.

The prize lies farther down the ballot: Both houses of the Arkansas legislature are in play this November, with every seat up for reelection for the first time in a decade.

Republicans need to flip just a handful of those spots to turn the chambers red for the first time since the end of the Civil War. If they succeed, it will be another death knell for Southern Democrats and perhaps the beginning of a new Solid South — of the 11 states that made up the Confederacy, only Arkansas still has a Democratic chamber.

Using a bus tour across the state, AFP is making its case for smaller government. It is fighting tax increases and curbs on development and is leading the charge against the creation of a state health insurance exchange, a key part of President Obama’s health-care law.

“These policies start in Washington, D.C., but they come to us in the state of Arkansas,” the group’s state director, Teresa ­Oelke, told a crowd of about 30 gathered recently in Paragould. “That’s where they’re implemented and that’s how they move forward.”

Drawn by robo-calls and a promise of free barbecue, the crowd stood outside a gas station and a motorcycle-themed res­taurant, next to a big green bus with two-foot-high lettering: “Obama’s Failing Agenda Tour.”

The presence of Americans for Prosperity in Arkansas this election season illustrates the ambitions of independent interest groups that are eager to leave a mark far beyond the presidential and congressional races.

Created in 2004 as a counterweight to unions’ grass-roots organizing, AFP is known for its hard-hitting TV ads attacking Obama and stirring tea party opposition to his policies. But it also is fully engaged in more local issues and races in 35 states, with a $100 million budget that is three times the 2010 figure.

In Virginia, the group fought the expansion of Metrorail service into Loudoun County. In Detroit, it is opposing construction of a new bridge to Canada, saying it is a poor use of taxpayer money.

AFP bolstered conservatives in Kansas when it helped defeat eight moderate Republican state senators this year. And it countered labor with door-to-door campaigning in Wisconsin to help Gov. Scott Walker (R) survive a recall attempt, at the same time advocating for a large new iron mine.

In Arkansas, Oelke and others are focusing their efforts against about a dozen Democratic state legislators who supported a proposed ballot measure to raise the tax on diesel fuel.

Among them is Robert Thompson, who represents Paragould in the state Senate and says the tax was never even put before voters. Such opposition is a new experience for Thompson, who ran unopposed in his last race here in northeastern Arkansas and faced only a primary opponent four years earlier.

“You didn’t have outside money coming in,” Thompson said, noting that a little money goes a long way in a state legislative race. “If any outside group comes in and spends $10,000, that’s a big chunk of what the candidates are going to spend.”

Arkansas Republicans need to win three seats in the Senate and five in the House to win both chambers. With such a tight balance of power, the new money coming in has created a spending arms race with the state Democratic Party and the national Democratic Legislative Campaign Committee, whose officials said they hope to spend more than $500,000 in the state.

Here and nationwide, AFP recruits volunteers to work phone banks and canvass neighborhoods. That differs from many of the largest conservative political groups, which spend their budgets almost exclusively on mass media.

Detractors charge that AFP, far from grass-roots, is a well-funded “AstroTurf” organization shilling for its corporate patrons and rich donors. But it is impossible to determine that, because the group does not have to publicize its finances or donors. Oelke and other officials counter that the money spent here is raised in the state, and they point to grass-roots supporters, which Oelke numbers at 63,000 in Arkansas.

In Paragould, the anti-Obama tour was not crowded with volunteers, just five paid staff members, including the driver. When the bus stopped in Jonesboro, more than 100 people came out.

The group has made an impact on the state legislature: In the May primaries, two GOP senators lost their seats to conservatives after AFP helped mobilize opposition to moderate Republicans.

Now, Democrats in state government are on the defensive, reacting to widespread distrust of the president. Daniel Ray, for example, got fired up at the rally in Paragould, saying he’s sick of federal government spending.

“I don’t think this election term I could vote for any Democrat,” said Ray, 35, who is “ashamed to say” he took a state government job for the benefits it offered for his family.

Ray, the father of four boys, knows Thompson and helped vote him into office, but said he’ll support the challenger this time, out of frustration with Democrats in Washington and Thompson’s refusal to denounce them.

“I don’t think you can be associated with someone with those values and not stand against them,” Ray said. “I don’t see him doing that and it offends me.”

The 60 Plus Association, another group with connections to the Koch brothers, has sent mailers targeting vulnerable legislators by linking them to the Democrats’ signature health-care law. State politicians, the mailer said, “voted to support Obama’s health care plan.”

“It’s another lie,” said Butch Wilkins, one of the targeted Democratic legislators who represents part of Jonesboro. “Of course I don’t have a vote on Obamacare.”

The mailer depicts an African American man in a lab coat with a stethoscope slung over his shoulder and cites a vote to accept federal funding for the state health insurance exchange. The group did not respond to requests for comment.

Obama has never been a popular figure in Arkansas. The state was one of only six in which his share of the vote in 2008 was less than Democratic nominee John F. Kerry’s in 2004. A largely unknown challenger to Obama, a lawyer from Tennessee, received 41 percent of the vote in this year’s Democratic primary.

The Arkansas unemployment rate is 7.3 percent, one point below the national figure, but the state remains one of the nation’s poorest, with some of the worst health outcomes.

Many people at the rallies said they came to hear actor John Ratzenberger, who played the know-it-all postman Cliff Clavin in the 1980s sitcom “Cheers.” Oelke hired Ratzenberger, who spoke on the dangers of political correctness and a need for more vocational training in schools. But he also wandered off message, saying repeatedly that his favorite politician was the late House speaker Thomas P. “Tip” O’Neill, who was a liberal Massachusetts Democrat.

In three northeast Arkansas towns, local Democrats protested, chanting Obama’s name.

“They call themselves Americans for Progress, but they want to take us back — kill Social Security, kill the 40-hour week,” said Gerald Bosacker, 82. “They want to take us back to slave labor. Democracy is at stake.”

Koch Industries, a Kansas petrochemical conglomerate, has interests in Arkansas, including a sprawling paper plant in downtown Crossett run by its Georgia Pacific subsidiary. The company employs more than a 1,000 workers there and in 2010 announced a $250 million expansion of the plant. Koch Industries officials declined to comment.

Democrats often accuse AFP of pushing policies that benefit its wealthy backers, including lower taxes and less government regulation.

“I call them Americans for Their Prosperity,” said Wilkins, the state representative. “They’re not interested in prosperity for Arkansas, but they’re interested in someone’s prosperity.”