WASHINGTON — It's been a constant quandary for the Obama White House: Should the president reach out to his Republican opponents or isolate them? Should he compromise to move his agenda or try to split the GOP ranks? Carrot or stick?

That debate appeared settled on Thursday when President Obama spoke in the White House State Dining Room to deliver his verdict on the just-ended government shutdown: more stick.

"To all my friends in Congress, understand that how business is done in this town has to change," Obama said as he praised "responsible Republicans" for brokering the deal but denounced "the pressure from the extremes."

He offered a blunt, almost taunting, message to his Republican opponents: "You don't like a particular policy or a particular president, then argue for your position. Go out there and win an election."

FULL COVERAGE: The U.S. government shutdown

When Republicans embarked on the strategy of shutting down government programs to win concessions from Obama, many said they expected the president to fold quickly. And many Democrats feared that would be true. But the White House set out to end the perception that it is too quick to make a deal.

"He just wasn't going to cave. The guy's been reelected, what does he need to cave for?" said Neera Tanden, president of the Center for American Progress, a liberal think tank with close ties to the White House. "The world is very different if you're never going to face voters again. You can hold strong and not be worried about it."

The budget deal Obama signed early Thursday included no significant concessions on Obamacare or government spending. Polls showed Republicans took the brunt of the blame for the debacle. The Republican Party came away from the confrontation demoralized and debilitated by the gulf between its tea party wing and its leaders.

But senior administration officials and White House allies also acknowledged that the winning strategy in this round of the budget battle may not translate into additional legislative successes. The deal only extended funds for government agencies until Jan. 15 and suspended the debt limit until Feb. 7.

The White House and Congress will almost immediately plunge into a new round of talks — and face the threat of another shutdown. In his remarks, Obama listed two other priorities for the year: immigration reform and a farm bill. Progress on all three issues still depends on whether Obama can work with Republicans and whether the party emerges from this standoff ready to compromise or more united in opposition.

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Administration officials acknowledge that's an open question — one Republicans have yet to answer.

Senate Minority Leader Mitch McConnell (R-Ky.) told the Hill newspaper that he would not allow a repeat. "There is no education in the second kick of a mule. There will not be a government shutdown," he said. "I think we have fully now acquainted our new members with what a losing strategy that is."

Still, as Obama pushed for a new spirit of cooperation, one key Republican was backing away burned.

Rep. Raul R. Labrador (R-Idaho), who played an influential role earlier this year working with lawmakers from both parties to write a bipartisan immigration bill, said he was unwilling to enter into talks over the controversial issue because of Obama's refusal to negotiate with House Speaker John A. Boehner (R-Ohio).

"After the way the president acted over the last two or three weeks, where he would refuse to talk to the speaker of the House … they're not going to get immigration reform. It's done," Labrador said.

In 2011, after a tense standoff while negotiating over raising the debt limit, Obama vowed never to do that again.

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Many internal discussions followed about what to do the next time, according to a senior administration official who asked not be identified while discussing strategy. Some within the West Wing argued that refusing to talk would be contrary to Obama's brand — and his personal inclination. They worried that it would be difficult to portray the president as reasonable if he was not willing to bargain.

In the end, the president was shielded from this line of criticism, in part by Republican missteps, the official said. The public viewed the demand to repeal the three-year-old healthcare law as the more unreasonable position.