TOPEKA, Kan. — Frustrated by their inability to achieve some policy goals, conservatives in Republican states are turning against moderate members of their own party, trying to drive them out of state legislatures to clear the way for reshaping government across a wide swath of mid-America controlled by the GOP.

Political groups are helping finance the efforts by supporting primary election challenges targeting several dozen moderate Republicans in the Midwest and South, especially prominent lawmakers who run key state committees.

Two years after Republicans swept into power in many state capitals, the challengers say it’s time to adopt more conservative policies.

“If you don’t believe in that playbook, then why are you on the team?” declared Greg Smith, a Kansas state representative who’s running for the state Senate, with the goal of making it more conservative.

The push is most intense in Kansas, where conservatives are attempting to replace a dozen moderate Republican senators who bucked new Gov. Sam Brownback’s move to slash state income taxes.

The Club for Growth, a major conservative interest group, is spending about $500,000 in Missouri this year. That’s double the amount it invested two years ago. The anti-tax group Americans for Prosperity opened new chapters in Iowa, Minnesota and New Mexico. The conservative business group Texans for Lawsuit Reform spent $3.5 million on legislative candidates in the first half of 2012, more than double its total during the same period two years ago.

The primary strife reflects differences that were somewhat concealed in the party’s triumphant victories in 2010, when, aided by public discontent about the economy, the GOP won its broadest control of state government since the Great Depression. After the vote, Republicans held governorships in 29 states and control of most of the legislatures from Michigan to Texas.

Conservatives, some aligned with the tea party movement, hoped to begin realizing their vision of smaller government and of a reformed education system that would give parents more alternatives to traditional public schools. But some of their initiatives were scaled back by GOP colleagues to soften the impact on public schools and other public services.

Oklahoma Republican Gov. Mary Fallin’s plan to begin phasing out the state income tax was blocked entirely, and Brownback and Nebraska Gov. Dave Heineman had to settle for a fraction of the tax cuts they wanted.

Conservative leaders say they are determined to seize a historic opportunity. Primary elections and runoffs are continuing in key states through August. The results so far have been mixed, with the overall effect this year likely to be incremental.

“It’s no secret that there’s kind of a battle for what the Republican Party will be into the future and, as a consequence, what this state will look like into the future,” said Mark Desetti, a lobbyist for the largest teachers’ union in Kansas.

The conservative push is being felt in states that are already solidly conservative, like Texas and Idaho, along with others, like Missouri, with a tradition of political moderation and divided power.

“Republican legislatures continue to move more and more to the right of center,” said Alan Cobb, who’s overseeing state-level operations for Americans for Prosperity. “You do have this tension everywhere.”

The conflict in Kansas is heading toward a showdown in the Aug. 7 primary. Conservatives want to oust Senate President Steve Morris, Senate Majority Leader Jay Emler and the leaders of most of the important committees in the state Senate, which acted as a check on Brownback’s move to make Kansas a laboratory of conservative fiscal and social policy.

“It is all about taking over the state in a conservative vein and eliminating as much as possible anybody who didn’t agree with their philosophical ideas,” said moderate GOP incumbent Sen. Tim Owens, one of the targets.

His opponent, conservative freshman state Rep. Jim Denning, said Owens has “lost his edge to lead, to negotiate, to stick to just Republican principles.”

The governor is taking the unusual step of formally endorsing some challengers because the moderates, in resisting his proposals, “promote a Democrat agenda,” he said.

The Kansas Chamber of Commerce raised $163,000 for the effort last year — a significant sum in a less populous state like Kansas — with more than $36,000 coming from Koch Industries Inc., the company led by Charles Koch, a prominent political donor.

So far this year, conservative challengers in Texas have unseated three state House committee chairmen who were accused by tea party adherents of cooperating with Democrats on legislation. A conservative opponent knocked off a moderate state senator in the Colorado primary.

In a key race in Missouri, David Pearce, the chairman of the Senate’s Education Committee, faces a Republican primary challenge next month from a conservative opponent who has received $50,000 from a major anti-tax group.

In Kansas, conservatives hope to win enough races to spur the legislature to restrict how labor unions raise campaign money, to remake the state’s appellate courts and to enact more conservative social policy. They’ve been disappointed that the state hasn’t moved new public employees into a 401(k)-style pension plan, and there’s been no serious consideration of school choice initiatives.