With the government shutdown and debt ceiling fight in the rearview mirror, Republicans can move on to more important matters — like determining which of the party's warring factions will control the GOP going forward.

The recent fiscal fist-fighting ostensibly pit Republicans against Democrats, but the real power struggle was between Tea Partiers and the GOP establishment. The conflict, bubbling beneath the surface for some time, finally boiled over into a messy public spat that, even as the shutdown came to a close, showed no signs of stopping.

The fissure has been growing since 2010, when the Tea Party ousted establishment candidates in favor of their own contenders. What was then a populist revolt has since rocketed congressional neophytes like Sen. Ted Cruz (R-Texas) to the forefront of the party's ideological and tactical debates, giving the hard right newfound legislative muscle. Just look at how Cruz and company dragged the party into a shutdown strategy that even Karl Rove said "no sentient being" believed would ever work.

As the shutdown came to a close Wednesday night, Cruz seized the microphone to mourn his failed strategy — and to once again lash out at his colleagues. In a bold display of hubris, he accused his fellow Republican senators of spoiling his gambit by "bombing our own troops."

Moderate establishment types struck back. Perhaps the oldest of the old guard, Sen. John McCain (R-Ariz.) — who called Cruz and his cohorts "wacko birds" earlier this year, and who criticized the shutdown tactic from the start — took a victory lap on Twitter.

Must-read @WSJ: "The Education of Ted Cruz - Some remarkable admissions from the 'defund' caucus" http://t.co/ghEswAnDkd — John McCain (@SenJohnMcCain) October 17, 2013

The GOP got burned badly in the shutdown fight, walking away with nothing to show for their efforts but a historically low approval rating. The only question left for them to answer in the aftermath is "who deserves to be written out of the movement going forward," as Politico's Alexander Burns put it.

For moderates, the answer is easy: Cruz.

"I think it's important for Republican leaders around the country to speak out against him and neutralize him," Rep. Peter King (R-N.Y.) said of Cruz. "Otherwise he's going to start the same nonsense again in December or January."

On the flip side, Tea Partiers blamed moderate Republicans for selling out the party. Powerful grassroots organizations that fomented the early Tea Party uprisings and who promoted the shutdown effort are driving that message home to movement conservatives.

FreedomWorks blasted the shutdown deal as a "full surrender" to Democrats. The Senate Conservatives Fund called Senate Minority Leader Mitch McConnell (R-Ky.) a "turncoat" and urged conservatives to oust him in a primary.

Likewise, National Review's Michael Walsh took issue with Sen. Lindsey Graham's (R-S.C.) contention that Republicans had to cave because they were losing so badly in the polls.

Graham's problems, of course, can be solved by the simple expedient of primarying him out of his Senate seat next year and replacing him with someone who understands the new normal of American politics, otherwise known as "fundamental transformation." This really is the best thing that could happen to him and his fellow accommodationists in Congress, since a loss to a Democrat would only reinforce their belief that conservatives are the real problem with that wing of the Permanent Bipartisan Fusion Party formerly known as the GOP, whereas a public humiliation at the hands of their own voters pour encourager les autres might actually do some good. [National Review]

It's in this environment that right wing figures like Sarah Palin and Red State's Erick Erickson have suggested conservatives break free and form their own party. The calls for a complete split "mark a new, more acrimonious chapter in the long-simmering conflict between the Tea Party and the Republican establishment," wrote The Atlantic's Molly Ball. While the two sides had coexisted through an odd marriage of necessity to this point, the Tea Party has grown increasingly tired of "feeling taken for granted by a party that alternately panders to them and sells them down the river."

The lingering animosity is only poised to worsen going forward. Each side is well-funded. And as a handful of hard-core conservatives showed in the shutdown, neither side has much of an institutional advantage either.

Furthermore, the big fiscal deal only funds the government through January 15 and hikes the debt ceiling to February, at which point we could very well replay the same bruising fight all over again.

McConnell said Thursday another shutdown was "off the table." Yet Cruz, on the very same day, said he would do it all again.

At some point, the GOP, for its own sake, will have to reconcile those competing visions for the party, represented respectively by the "suicide caucus" and the "surrender caucus." There is plenty of middle ground where the two can and have met before, but the wide divide between them, laid bare by the shutdown, is a raw wound neither side seems intent on closing any time soon.