FILE - This March 2, 2013 file photo shows Republican strategist Karl Rove,of American Crossroads, speaking in Sacramento, Calif. Virtually unknown outside Washington, a coalition of hardline conservative groups are fighting to seize control of the Republican agenda. (AP Photo/Rich Pedroncelli, File)

WASHINGTON (AP) -- Virtually unknown outside Washington, a coalition of hardline conservative groups is fighting to seize control of the Republican agenda.

Tea party allies like the Club for Growth, FreedomWorks and Heritage Action for America showed their might by insisting that the GOP embrace the government shutdown that hurt the nation's economy and the party's reputation.

Now emboldened, these groups are warning that their aggressive agenda-pushing tactics aren't over — and they're threatening retribution against Republicans who stand in their way.

"They refuse to learn," Chris Chocola, a former Indiana congressman who leads the Club for Growth, says of lawmakers who buck the will of right-leaning groups. He predicts that his group will support primary challengers to more than a dozen Republican incumbents seeking re-election next fall.

Mainstream GOP groups — such as Karl Rove's American Crossroads or the party's formal campaign committees — question their more conservative counterparts' role, fed up by their outsized influence in shaping the party's current agenda.

For decades, interest groups like the National Rifle Association have shaped debates on single issues. But Republicans suggest that not since the Christian Coalition of the 1990s have outside forces played such a sweeping, integral role in guiding Republican priorities as the tea party-led fiscal conservatives have in the ongoing budget debate.

"You have a small group in Congress that has become the surrender caucus," argues Illinois Rep. Adam Kinzinger. "They've surrendered their voting card to the wishes of these outside groups."

Such divisions on display between the Republican Party's pragmatic and ideological wings — and their affiliated outside groups — carry huge risk for the GOP heading into the 2014 midterm congressional elections. Republicans will seek to win power in the Senate and preserve their narrow House majority next fall.

But primaries that leave eventual nominees battered and broke for the general election could hamper that goal.

Nevertheless, tea party-aligned groups already are spending millions of dollars calling on compromise-minded Republican lawmakers from New Hampshire to Idaho to embrace more aggressive tactics against President Barack Obama's agenda.

This is their message as Congress wrestles with health care implementation, considers immigration reform and gets ready for new rounds of debt talks: Republicans who work with the Democratic president do so at their peril.

It appears that no Republican is too large for these groups.

The Senate Conservatives Fund — founded by tea party hero and former South Carolina Sen. Jim DeMint — has launched television ads against Republican leaders, including Senate Minority Leader Mitch McConnell of Kentucky, who helped craft the recent budget compromise that ended the shutdown. It also has criticized Sen. Jeff Flake of Arizona and Sen. Jonny Isakson of Georgia.

The Club for Growth also is targeting Oregon Rep. Greg Walden, despite his role as leader of the campaign committee charged with preserving the Republican House majority. The group already has launched a website entitled, "Primary My Congressman," and so far identified 10 potential campaigns to unseat Republican incumbents.

That group and others also are spending hundreds of thousands of dollars to support a challenge against longtime Republican Sen. Thad Cochran, of Mississippi, in hopes of persuading him to retire. And the Tea Party Patriots is going after Sen. John Cornyn of Texas, Sen. Mark Kirk of Illinois and Sen. Kelly Ayotte of New Hampshire.

Behind the scenes, GOP campaign officials are urging donors to fund mainstream groups to counter the conservative outfits. These officials are doing so even as they question the right-flank's ultimate effectiveness, given that its groups, although vocal, typically have far less money compared with other organizations standing with Republicans from the establishment wing.

The most powerful Republican allies from the last election — mainstream Republican groups such as the U.S. Chamber of Commerce, American Crossroads and its sister organization Crossroads GPS — poured more than $212 million combined into the 2012 election. Combined, the Club for Growth, Heritage Action and the Senate Conservatives Fund spent $21 million.

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