A defeated GOP wants to unite, move on, fight another day

But, even in defeat, many who were in the room say there was a surprising feeling of unity. On that night, 16 days into their failed strategy, the diverse group of Republicans who have had sharp differences on how to push a Republican agenda in a Democratic led government stood as one.

House Majority Leader Eric Cantor, R-Virginia, spoke passionately in the GOP conference room, urging his members to unify. And it worked. Embattled Speaker of the House John Boehner received a standing ovation. The unusual plea for unity was a recognition that the last few weeks had been, to say the least, bruising for the GOP.

The government shutdown exposed major divisions in the party.

During the summer, the far right tea party wing had backed Boehner into a corner by demanding he link defunding the Affordable Care Act, also known as Obamacare, to the shutdown and debt ceiling. Meanwhile, what was left of the Republican moderates in the House and Senate -- in fact much of the more realistic GOP center -- had privately thought the tactic would lead to political disaster.

And they ended up being right.

"I think we have fully now acquainted our new members with what a losing strategy that is," Senate Minority Leader Mitch McConnell of Kentucky told The Hill.

On some issues, Republicans are likely to motivate around common themes.

As talks with Democratic leaders get underway on a budget, Republicans are likely to stand against any effort to raise taxes and will push for lower government spending and changes to entitlement programs.

And Republicans have turned their attention to another aspect of Obamacare: its chief implementer, Health and Human Services Secretary Kathleen Sebelius. The GOP is calling for her resignation over its botched rollout.

While the Republicans stood united in the face of defeat, the day-to-day realities are going to prove much more difficult.

The President is already pushing Congress to get started on immigration reform, which the Senate already passed. Immigration has long been a contentious subject within the Republican Party. Some members are opposed to any liberalization of immigration laws while others, including former President George W. Bush, have pushed the party to embrace a comprehensive overhaul.

In the two days after that showing of unity, fractures are already forming.

McConnell said this week that he will not allow another partial government shutdown.

"One of my favorite old Kentucky sayings is there's no education in the second kick of a mule," he told the Hill newspaper. "There will not be a government shutdown."

But an aide to Texas Sen. Ted Cruz said he had a different point of view. The aide told CNN's Dana Bash that he has not ruled out any future efforts to shutdown the government in the fight against Obamacare.

Additionally, Cruz blamed his Republican Senate colleagues for losing the fight.

"Unfortunately, the Senate chose not to follow the House. And in particular, we saw real division among the House of Representatives. That was unfortunate. I would point out that had Senate Republicans united, and supported House Republicans, the outcome of this, I believe, would've been very, very different," Cruz told CNN's Dana Bash.

While Cruz gained national attention -- and much condemnation -- for his fight, his support among tea party activists has skyrocketed to 74%. But at the same time, support for the tea party declined with only 30% of Republicans viewing the coalition favorably, according to Pew Research Center.

It's a paradigm Republicans have to consider as they hope to maintain control of the House and obtain control of the Senate in the 2014 elections and win the White House in 2016.

That's something with which McConnell, a political veteran, is well aware. "Full-scale repeal is obviously something that's not going to be achievable until I'm the majority leader of the Senate and we have a new president," he told the Hill, referring to a repeal of Obamacare.

But McConnell has a tough re-election of his own. And conservative activists are not pleased with his role in negotiating a deal to reopen the government. The Senate Conservative Fund, a group dedicated to electing conservative members of the Senate, endorsed his challenger, Matt Bevin, Friday morning.

One of the lawmakers who backed the strategy to defund Obamacare, Rep. Ted Yoho of Florida, said that the fight was worth it.

"If we don't address it today, when are we going to address it?" he rhetorically asked on CNN's 'Erin Burnett OutFront."

But on the same program, fellow Republican Rep. Michael Grimm of New York said the GOP is "a big party," adding that a lot of members believe in being "pragmatic and reasonable," noting that the strategy to dismantle Obamacare was neither.

As politicians often look for political advantage, Obama highlighted the Republican divisions.

"We shouldn't fail to act on areas that we do agree or could agree just because it's bad politics, just because the extremes in our party don't like the word compromise," he said Thursday.

Boehner, who has spent the last two-and-a-half years trying to corral his party on a host of issues, knows full well the difficulty of uniting the party.

"Because we're Republicans, we're a little more independent-minded than our friends across the aisle," Boehner told WLW radio Wednesday. "Some are a little bit more independent-minded than others."