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. His group is already seeking or supporting primary challengers for 10 congressional 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.

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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.

National GOP officials are watching for signs of rifts among the right-leaning groups, which could dilute their power. The shutdown debate itself exposed at least one disagreement.

The Club for Growth, FreedomWorks and Heritage Action for America defiantly insisted that any deal to end the shutdown and raise the nation's debt ceiling must dismantle or delay Obama's health care law. Lawmakers who didn't stand them with them risked inviting primary challenges.

But some tea party allies like Americans for Prosperity, the group funded by conservative billionaires Charles and David Koch, opposed the tactics that led to the shutdown. Now that group is trying to move on, investing $2 million in a four-state ad campaign that hammers Democrats over the troubled health care law implementation.

"We're convinced that repealing Obamacare is long-term effort," AFP president Tim Phillips says, explaining why it didn't sign onto the right-flank's demands to defund the law as part of a budget compromise.

In a sign of another possible crack in the conservative coalition, a spokesman for Heritage Action for America says that in the near future, it likely will focus its health care criticism on Democrats, who stood together during the shutdown debate.

"There needs to be some breaks in that unity," says Heritage spokesman Dan Holler. "That may happen naturally, or it may need to be forced."

But Chocola said the Club for Growth wouldn't stop pressuring Republicans, particularly as congressional leaders begin to debate a new budget package.

Chocola wouldn't rule out another push to link such legislation to the president's health care law, but said his group might shift its strategy if major shifts to entitlement programs are included.

As the possibility of a shutdown loomed large in September, the network of GOP outside groups disagreed over strategy.

Crossroads officials briefed members of Congress on internal polling that showed the shutdown strategy deeply unpopular. Given that, the group and its fellow mainstream Republican allies largely stayed silent, fearing influential talk show radio hosts and aggressive conservative activists would brand them as heretics.

Meanwhile, conservative groups grew even more vocal in pressuring House and Senate Republicans to refuse to budge from tea party demands to defund "Obamacare" as part of any budget deal.

Eventually, House Speaker John Boehner broke with the right flank and endorsed the bipartisan plan to end the 16-day shutdown and raise the debt limit. And 87 Republicans in the House and 18 in the Senate supported it.

The damage to the GOP was severe: a Washington Post-ABC News poll found that 63 percent of Americans now have a negative view of the Republican Party, the worst rating for the GOP in almost three decades.

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Follow and Steve Peoples on Twitter: https://twitter.com/sppeoples and Philip Elliott: http://www.twitter.com/philip_elliott