The same conservative activist groups that continue to cause the GOP establishment so much heartburn are approaching the 113th Congress and the 2014 election cycle with what might appear to be a surprising level of sobriety and realism.

To varying degrees, these organizations acknowledge the limits of Republican power in Washington, recognizing that the GOP House majority cannot dictate to a Senate and White House controlled by Democrats, and they concede that their own process for recruiting candidates and influencing Senate races needs refinement and improvement. They also gently chide their congressional conservative allies who, while heeding calls to oppose particular legislation, haven’t always done so with a political strategy in mind for persuading voters.

With the debt ceiling fight immediately at hand, leaders of the Club for Growth, FreedomWorks and Heritage Action for America told CQ Roll Call that while the perfect outcomes they advocate might not be achievable on this or other issues during the next two years, Republicans can still accomplish much. What they want are GOP leaders willing to fight and Republicans across the spectrum who prioritize a concerted strategy for winning broad public support over playing Beltway politics with Democrats.

“You have to win the battle of ideas,” said Club for Growth President Chris Chocola, whose group with its reputation for targeting incumbents in GOP primaries inspires perhaps the most fear among House Republicans. “There is a limit to what Republicans can do — they have the House, that’s it. But they can engage in the battle of ideas to the point where they can expose the other side.”

In the aftermath of President Barack Obama’s re-election and Democrats expanding their Senate majority, Washington’s well-known tea-party-affiliated organizations — including the club, FreedomWorks and Heritage Action, among others — are hardly going soft. Key votes against undesirable legislation, such as disaster relief for victims of Superstorm Sandy, not to mention the bipartisan deal averting the fiscal cliff, continue apace, and the threat of targeting perceived wayward Republicans in the 2014 House and Senate primaries remains.

But in terms of recognizing what the House Republican majority can actually push through a Democratic Senate and get Obama to sign, realism pervades. How congressional Republicans respond to this opposition is what most concerns conservative groups. It’s hard to tell what kind of deal on the debt ceiling and other matters the groups might find acceptable — and whether they’ll agree amongst themselves as to what that is.

There was a consensus, however, on bringing back regular order in the House to pass legislation that 218 Republicans can agree on and letting that serve as the GOP’s negotiating position on matters such as the debt ceiling. And, when Senate Majority Leader Harry Reid informs Speaker John A. Boehner that the bill is unacceptable, they want the Ohio Republican to eschew private talks and tell the Nevada Democrat that his conference will only accept a counteroffer in the form of legislation.

“The frustration from conservatives is when you never have a chance to have the conflict,” Heritage Action CEO Michael A. Needham said. “There’s something about going behind closed doors that sends a message that you’re not really trying to win an argument with the American people.”

This issue of “regular order” appears to be of primary importance to conservative activists, with comments about being willing to force a policy debate with the Democrats, and using the legislative process to do so, arising unprompted in interviews with Chocola, a former Indiana congressman, as well as Needham and FreedomWorks President and CEO Matt Kibbe, who served as a House Budget Committee aide in the 1990s.

As if for emphasis, Kibbe and Needham praised the government spending bill that was passed by House Republicans early in 2011 and the fiscal 2012 budget plan of House Budget Chairman Paul Ryan, R-Wis., in large part because each bill cleared the House under regular order. Needham noted that Heritage Action did not make the spending bill a key vote despite its belief that it fell short on policy, primarily because it was debated under regular order.

Chocola joined Kibbe and Needham in saying that a key change they would like to see from House Republicans in the 113th Congress is not just a return to regular order, but also a refusal to abandon the bills they pass through that process in favor of closed-door talks with Reid and the Obama administration, as they did during the debates over the 2011 debt ceiling increase and the fiscal cliff.

A priority for these tea-party-friendly groups is how Republicans go about selling their plans. While they volunteered plenty of criticism for Boehner and other congressional GOP leaders, some of the conservatives interviewed for this story confirmed, albeit gingerly, that they believe their stalwarts in Congress have failed to offer — during the fiscal cliff debate, at least — a coherent, unified and appealing message to persuade voters to side with them on fiscal issues.

Just voting “no” with the comfort that their gerrymandered district agrees with them is not a strategy, nor is it politically helpful, some acknowledged.

“You can’t beat a bad idea with nothing,” Kibbe said. “We seem to get into these fiscal wars without any ideas in our quiver.”

Electorally, the Club for Growth, FreedomWorks and Heritage Action say it’s too early to tell how active they will be in the 2014 elections and how much of their efforts will go to targeting incumbents in primaries. Chocola said he is pleased with his organization’s 2012 record, ticking off the list of GOP-establishment-backed candidates who lost on Nov. 6, suggesting the club’s record would be pristine if not for Richard Mourdock’s Senate loss in Indiana.

But Kibbe was candid about his belief that conservative activist groups, including his own, could improve their Election Day showing if they work harder to identify candidates who fit their policy profile and are also capable politicians who know how to win. And he suggested that one way to go about that might be to recruit good candidates, rather than simply choosing from the most conservative candidate who happens to run.

“There is huge room for improvement,” Kibbe said.