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Representative Adam Kinzinger, Republican of Illinois, would seem to be just the kind of promising politician his party needs at this stage: a telegenic, 35-year-old former Air Force pilot, close to members of the House leadership and an effective campaigner who won easily in both 2010 and 2012.

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But to the Club for Growth, the conservative group intent on electing candidates who adhere strictly to a small-government, low-tax philosophy, Mr. Kinzinger falls short.

The group is featuring him on a new Web site intended to promote primary challenges next year to Republican incumbents who it believes have compromised on conservative principles. In Mr. Kinzinger’s case, the group said, his failures include going along with the bipartisan agreement in 2011 to raise the federal debt ceiling and voting with Speaker John A. Boehner to ratify the deal at the beginning of this year to raise taxes on the wealthy but avert tax increases for the middle class.

As the Republican Party and the conservative movement continue to debate the lessons of 2012 — a discussion that will get further attention this week at the annual Conservative Political Action Conference in Washington — the Club for Growth is playing the role of principle-driven counterweight to Karl Rove, whose political operation has been leading the charge favoring of a more pragmatic view of how Republicans can best regain power.

It is a stance that has made the group and its president, Chris Chocola, beacons of conviction to economic conservatives who think the party’s Congressional leadership has been too willing to make deals and back moderate candidates. But the Club for Growth’s strategy has also exacerbated strains within the party and drawn criticism that ideological conformity is the wrong formula for a party seeking to broaden its appeal in the wake of successive losses in presidential campaigns.

“I have always been concerned with the Club for Growth’s mission,” said Rich Galen, a Republican commentator and former aide to Newt Gingrich and Dan Quayle. “As someone who came to Washington after Watergate when the House G.O.P. could meet in a phone booth, I have always felt it is too hard to elect our folks to put them at risk in primaries.”

To be a broad-based majority party, Mr. Galen said, “you have to accept that the edges will get farther and farther apart and you have to accept that one edge will not agree on all items with the other edge — but they will agree more with that other edge than they would with Democrats.”

To Mr. Chocola, that kind of attitude is exactly the problem.

“I can’t go to the Capitol Hill Club anymore,” he said, referring to the hangout for House Republicans. “But we have a $16 trillion debt because politicians worry about being popular rather than providing the leadership to do the hard things.”

Mr. Chocola’s argument is that the path to success for Republicans is to embrace sharp ideological differences with Democrats rather than sanding them down, even in states and districts that do not inherently lean conservative. As models, he points to Senators Marco Rubio of Florida and Patrick J. Toomey of Pennsylvania, Republicans who won their seats in 2010 in states that President Obama carried in both 2008 and 2012.

In an interview, Mr. Chocola dismissed the idea that Club for Growth and other conservative groups were responsible for losses in Senate races last year in Missouri and Indiana, where the Republican candidates, Todd Akin and Richard Mourdock, both collapsed after making statements about rape. His group had backed Mr. Mourdock but not Mr. Akin.

“Richard Mourdock and Todd Akin lost because they said stupid things,” said Mr. Chocola, a former Republican member of the House.

“The real question is Heather Wilson, Tommy Thompson, George Allen, Denny Rehberg – why did they all lose?” Mr. Chocola said, referring to Republican candidates for Senate in 2012 in New Mexico, Wisconsin, Virginia and Montana. “If you have these kinds of establishment-backed Republican candidates who lost, in some cases in states where Romney won, that’s a more interesting question and one that ought to be the focus of the party. I think the answer is that you just need candidates who are willing to articulate a clear, convincing, conservative economic message and aren’t afraid of what Republicans are supposed to stand for.”

Mr. Chocola said he did not see the Club for Growth being in a fight for the soul of the party with Mr. Rove’s group. “But if they want to create a Republican primary establishment-versus-conservative battle, the conservative’s going to win,” he said.

It is not clear how aggressive the Club for Growth will be in fielding conservative challenges to Republican incumbents this year. Mr. Chocola said the group prefers to back candidates who have already decided to run rather than recruiting challengers to take on incumbents, and that it studies races carefully before jumping into primaries to ensure it is behind candidates who have a shot at winning.

“People ask about Lindsey Graham and Lamar Alexander and Mitch McConnell,” he said, naming three incumbent Republican senators who are up for re-election in 2014 and are viewed as ideologically wobbly by some conservatives. “We’re risk takers. But there are a lot of dynamics that have to be in place for us to engage in a race like that.”

“We don’t just do it because we like to make people miserable,” he said. “We do it because we think there’s a good chance of getting a champion of economic freedom in that seat.”

The Club for Growth’s supporters said the group helps the conservative cause even when it does not put its considerable financial clout behind a candidate, because the mere threat of a primary challenge keeps some Republicans from drifting into the political center. They said the group’s advocacy of moving more aggressively to balance the budget in 10 years was one reason that Representative Paul D. Ryan offered a plan this year to do just that. Mr. McConnell, leery of the potential for a Tea Party-inspired primary challenge against him, has hired the campaign manager employed in 2010 by Senator Rand Paul of Kentucky, a Tea Party favorite.

For now, the Club for Growth is looking for smaller opportunities, chiefly among incumbent House members who are in safe Republican districts but have voting records that the group deems insufficiently conservative on the issues it cares most about — primarily, matters of taxes and spending.

In Mr. Kinzinger’s case, Club for Growth gave him a 56 percent rating on its voting scorecard in a district that Mr. Romney carried with 53 percent of the vote — the kind of district that Democrats would need to put in play if they are to have a chance of winning back control of the House.

“We’re not concerned with an out-of-touch D.C.-based PAC that, time after time, unsuccessfully attempts to force their Washington agenda on Illinois families and businesses,” said Brook Hougesen, Mr. Kinzinger’s spokeswoman.