Has the Tea Party been tamed?

Establishment Republicans are crowing that their resounding wins Tuesday night repudiated the Tea Party’s insistence that ideological purity is key to electoral success. 

But don’t tell that to conservatives, who aren’t admitting defeat. 

In fact, they’re claiming victory on the issues, if not for the candidates themselves, and pledging future fights to hold the GOP-led Senate accountable if senators stray from their campaign promises.

“Every single Republican ran as a conservative,” Brent Bozell, chairman of ForAmerica, told The Hill. “Name me one moderate issue that won. Moderation was defeated everywhere.”

The numbers don’t bear that out. The national party made an early and aggressive play to neutralize conservative challenges and make sure the most electable candidates won the party’s nominations, to great effect.

"We said we were going to be the Nick Saban of recruiting, we were going to recruit the best candidates, put them in the right position,"  National Republican Senatorial Committee Political Director Ward Baker told reporters Thursday. "We decided we couldn't be Akin-ed anymore. No more witches, no more gaffes."

In the end, conservatives won just one of their competitive primary fights in the Nebraska Senate race, lost all of their incumbent challenges and worked with establishment Republicans to support less-than-ideal candidates to achieve the shared goal of taking back Senate control.

And there was no indication their absence on Tuesday night would’ve made much of a difference for Republicans. Even those GOP candidates initially most abhorred by the conservative grass roots, like Sen. Pat RobertsCharles (Pat) Patrick RobertsRural America hopes Trump hasn't forgotten his promise Republicans slam Trump's tariffs plan Senate Republicans float legislation to reverse Trump tariffs MORE (Kan.) and Senate GOP leader Mitch McConnellAddison (Mitch) Mitchell McConnellSenate tees up Yemen vote for Tuesday Senate confirms Trump's border chief House leaves out ObamaCare fix from must-pass funding bill MORE (Ky.), delivered decisive double-digit wins.

Still, leaders from a handful of major conservative groups took credit for those wins during a Wednesday press conference, arguing the success was due to the winning Republicans running on a “conservative” platform of ObamaCare repeal, balancing the budget and opposition to "amnesty" for illegal immigrants. They all demanded Republicans hold to those promises when they take control of the Senate.

Conservative fervor has cooled somewhat on repealing ObamaCare. They said they’d be happy enough with simply sending bill to repeal the law to the president’s desk and forcing him to veto them, even if that effort doesn’t bear fruit. 

“If a bill repealing ObamaCare passes the House and passes the Senate and goes to the president and he vetoes it, I don’t know how we can be upset with a bill that does exactly what we asked them to do,” Citizens United President David Bossie said.

A broader debate building within the party, over the scope of GOP policy goals, could exacerbate tensions. Both McConnell and Speaker John BoehnerJohn Andrew Boehner4 reasons Mike Pompeo will succeed at Foggy Bottom The misunderstood reason Congress can’t get its job done GOP sees McCarthy moving up — if GOP loses the House MORE (R-Ohio) have said they want to initially pursue smaller, bipartisan accomplishments, like approving the Keystone XL pipeline and a bill meant to encourage the hiring of veterans.

But Brian Phillips, communications director for Sen. Mike LeeMichael (Mike) Shumway LeeSenate tees up Yemen vote for Tuesday Congress moving to end US involvement in Yemen This week: Congress races to prevent third shutdown MORE (R-Utah), who chairs the Senate Steering Committee, said conservatives are concerned that the GOP will get stuck on what he called “small-ball items.”

“The message that conservatives are sending to the new GOP majority is, we can’t just do small-ball items and we can’t just do the things K Street wants us to do even if they’re good policy. We have to make as much a part of our agenda as anything larger reform bills that speak directly to middle class families and working class Americans,” he said.

Phillips listed welfare and education reform as two bigger-picture items conservatives want to see on the agenda, and others have emphasized tax reform as well.  

He said he doesn’t see the same sorts of internecine warfare blowing up the legislative process now that Republicans control the Senate. Those battles — like the one that led to the government shutdown — were largely “tactical,” over the “how” of stopping President Obama’s agenda.

“We’re in charge now. We don’t have to fight over the tactics. What we’re going to be debating in the caucus is the substance of the bills, about the right way” to do reforms, Phillips said. “That’s a great debate to have in front of the American people.”

Phillips said early discussions outlining priorities for reform have been happening for the past year with many of the potential committee chairmen, and that “we don’t need McConnell to be in every one of these meetings.”

“It’s his job to get the votes,” he said.

But that may portend even fiercer and more high-profile policy fights within the party, especially as three prominent Republican senators who have been out front on policy debates before may be jockeying for an advantage in the 2016 GOP presidential primaries.

If Sens. Ted CruzRafael (Ted) Edward CruzOvernight Tech: Facebook faces crisis over Cambridge Analytica data | Lawmakers demand answers | What to watch for next | Day one of AT&T's merger trial | Self-driving Uber car kills pedestrian The case for a new branch of the military: United States Space Force The problem with hindsight MORE (Texas), Rand PaulRandal (Rand) Howard PaulTrump informally offered Cohn CIA job before changing his mind: report Congress moving to end US involvement in Yemen Congress races to finish .2 trillion funding bill MORE (Ky.) and Marco RubioMarco Antonio RubioRubio: McCabe 'should've been allowed to finish through the weekend' For Tillerson, bucking Trump became a job-killer At least six dead after pedestrian bridge collapses on cars in Florida MORE (Fla.) do decide to run, they’ll likely try to take leading roles in the GOP’s efforts to craft a legislative agenda and governing vision for the nation. But all have distinct visions of their own, and the prospect of the three battling for prominence could pull the party in three very different directions.

FreedomWorks Vice President Adam Brandon predicted as much, noting with Lee as chairman of the Steering Committee, “there’s going to be an opportunity to put some really kick-ass policies on the floor of the Senate ... and that will set up for 2016 a real difference in opinions.”

Cruz is already hinting at his own vision for the GOP-led Senate, focused on what he sees as Obama’s “lawless” executive action.

And many conservative priorities are likely to be unpalatable to Obama and Democrats. Those policy debates could jam McConnell between his expressed openness to compromise and conservatives’ visions of governance.

Immigration reform, which no conservatives mentioned as a top priority, remains one for the party overall, as Republicans see it as necessary if they hope to compete for Hispanic voters and succeed in national elections. There, conservatives’ insistence on opposition to giving illegal immigrants some form of citizenship is a nonstarter for Democrats and likely to stall any potential compromise Republicans hope to pass.

Indeed, a battle may already be looming over the immigration issue, as Cruz, Lee, and a handful of other senators warned that if Obama takes executive action on deportations they’ll “use all procedural means necessary” to focus the rest of the lame-duck session on that issue alone, potentially stalling any legislative activity during that time and setting up the possibility of another shutdown.

Further complicating the coming debate over policies and priorities is the fact that conservatives are already looking at the next House and Senate battles, unbowed by the failures of the current cycle. 

Bossie said his group has named three Republican incumbents ripe for a primary challenge, one senator and two House members, and Tea Party Patriots’ members are discussing their 2016 targets as well. Unlike 2014, it’s the GOP who faces a much tougher map in two years. 

Bossie hinted that even some of the Tea Party's favorites that were swept in on the wave of 2010 could be up for a challenge in the 2016 cycle.

"We look around now and we are not as happy with some of those members as we once were, because they come here and they get co-opted by leadership," he said.

"Would I support them? I don't know. They have to actually do what they promised to do."

Cameron Joseph and Ben Kamisar contributed.