With the sighs of relief came the immediate realization. When President Barack Obama signed a budget-battle-ending bill Wednesday night, he staved off these fights for three and four more months, respectively.

Another possible shutdown. Another possible brinkmanship game with default hanging in the balance. Or will next time be different?

There is no disputing that the shutdown and debt-ceiling debates have fractured the Republican Party, in more ways than one. The party is more unpopular now than at any time in at least the past two-plus decades, according to multiple polls. Moreover, they are split internally — the dispute over whether to defund the Affordable Care Act created another rift in the ongoing party civil war.

There's also no question that the conservative groups and politicians that began the debate over Obamacare say they are more fired up than ever to keep going.

"Nothing has changed," said Dan Holler, the communications director for Heritage Action, a key conservative group that led the fight to defund Obamacare, starting all the way back in July.

"It's unclear what the ground will look like, come December or January or February and beyond," Holler told Business Insider. "But certainly, if there is an opportunity to leverage the legislative process to protect some of the American people from Obamacare, that's something we should certainly do."

Erick Erickson, the editor of RedState, struck a similar tone on Thursday. The Senate Conservatives Fund is gearing up to make endorsements for the 2014 elections — and, spoiler, they're mostly (if not exclusively) going to endorse politicians who voted, or would vote, to defund Obamacare.

Meanwhile, the Republican politicians who engineered the fight over Obamacare that ultimately led to the shutdown aren't backing down. Sen. Ted Cruz (R-Texas), who gave a famous 21-hour speech during the debate, wouldn't rule out another shutdown.

Speaking to ABC's Jon Karl, he had a similar line as Heritage Action.

“I would do anything, and I will continue to do anything I can, to stop the train wreck that is Obamacare,” Cruz told Karl. “The test that matters, Jon, is are we doing anything for all the people that are getting hurt from Obamacare?”

Conservatives in the House held a similar line. Rep. John Fleming (R-La.) said in a statement after the bill passed the House that it moves the debate to "Round 2." Rep. Tim Huelskamp (R-Kan.) said Republicans are "winning the war."

For the shutdown and debt-ceiling threats to really be lifted requires a fundamental change from this debate — that GOP leadership does not give into plans led by Cruz and other conservatives; which, incidentally, leadership always said was doomed.

Senate Minority Leader Mitch McConnell, who helped broker the final budget deal on Wednesday, took that kind of firm stance on Thursday.

"One of my favorite sayings is an old Kentucky saying, 'There’s no education in the second kick of a mule,'" McConnell told National Review's Robert Costa. "The first kick of the mule was in 1995; the second one was the last 16 days. A government shutdown is off the table. We’re not going to do it."

Will McConnell's stand hold up? There's reason to be a little skeptical. For one, in the same interview, he said he knew in July this strategy wouldn't work. That might provide a lesson for the next time around — but when he'll be in the heat of a primary challenge for his Senate seat, will he really defy conservatives on Obamacare and/or vote to cleanly raise the debt ceiling?

Holler brought up the example of the Budget Control Act and the sequester cuts, which came from the 2011 debt-ceiling fight. McConnell has cited keeping the caps of the sequester in place during this round of budget battles as a major victory for Republicans.

"As Sen. McConnell has said, it's undeniable that debt ceiling can be extremely productive to advancing good policy," Holler said. "I don't think people are going to be willing to take it off the table. If you want to have some sort of impact on the legislative process, it's a tool you should use."