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Republican supporters cheered a speech at the Heritage Action for America forum in South Carolina on Friday.Credit Sean Rayford/Getty Images

GREENVILLE, S.C. — Gov. Scott Walker, eager to jump-start a flagging campaign, expressed support for a government shutdown over Planned Parenthood funding and likened his fights with lawmakers in Wisconsin to the movie “Braveheart.”

Jeb Bush reveled in the weeds of his tax plan and federal discretionary spending, appearing grateful for the chance to address a policy forum — until a discussion of his long-held support for Common Core education standards inspired hearty boos. “Hang on a second,” he pleaded. “You’re going to like the ending of this story.”

And Ben Carson, the retired neurosurgeon ascending in recent weeks toward the top of the polls, brandished the understated charm that has powered his rise: He entered to a standing ovation, thanked his hosts for inviting him on the day he was turning 64, and was promptly serenaded by the crowd with a full rendition of “Happy Birthday.”

“People think doctors only know medicine,” he said later, defending his qualifications as far-reaching. “They’re nuts.”

Two days after their second televised debate scrambled the race anew — perhaps most notably elevating the profile of Carly Fiorina — nearly all the Republican contenders for president descended on South Carolina on Friday for a conference organized by the conservative group Heritage Action for America. (The group is the political arm of the Heritage Foundation, founded in 1973 and transformed in recent years from a staid policy incubator to an organizing engine fueled by the Tea Party movement.)

The most striking exception was Donald J. Trump, who had been scheduled to appear. His campaign said that a pending business transaction had forced him to cancel, a development that Heritage Action called “unfortunate.” (Mr. Carson joked that the news of Mr. Trump’s dropping out was the “best birthday present.”)

In his absence, Mrs. Fiorina, propelled on Wednesday by a memorably steely exchange with Mr. Trump over his disparaging comments about her looks, moved to build her case as a top-tier candidate. (One of Heritage Action’s moderators, Gov. Nikki R. Haley of South Carolina, quipped of Mrs. Fiorina, “This is what a smart, intelligent face looks like.”)

In her own comments, Mrs. Fiorina cited her history as an executive, including her history interacting with China, in a forceful call to action that earned several sustained ovations.

“Pressure applied by citizens on their representatives will move the system,” she said. “President Fiorina will call on you as citizens of this great nation to take our government back.”

Mr. Bush, who was generally received warmly, cast himself as “a disrupter in Tallahassee” during his time as governor, suggesting his peers had comparatively thin résumés.

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“There are people who have been elected to Congress who have done a good job fighting President Obama, but they’ve never actually passed a law,” he said, urging people to “look at the governors” for records of true accomplishment.

In her questioning, Ms. Haley spoke particularly warmly of a fellow governor, Mr. Walker, and his bruising battles with union leaders in Wisconsin.

Mr. Walker, who again complained of his limited speaking time during the debate, drew sustained cheers during a discussion of Planned Parenthood. He said he supported attempts by Republicans in Congress to try to strip the group of federal funding, even if that leads to a government shutdown.

Mr. Walker emphasized what he described as his battle-ready toughness, hyperbolically likening his fight with members of his own party in the Wisconsin State Legislature to the bloody Mel Gibson biopic.

“It was kind of like I had the face paint on,” he said. “I had the battle charge ready.”

Yet few candidates could claim the reception earned by Mr. Carson from the several thousand people who attended the gathering in the Bon Secours Wellness Arena here. In contrast to several of his competitors, whose appearances on stage were preceded by slick introductory videos, Mr. Carson prepared a segment of ostensibly low production value: chiefly, Mr. Carson speaking into a single camera.

Once on stage, he described, at Ms. Haley’s urging, a youthful indiscretion: identifying as a liberal long ago, after spending formative years in Detroit and Boston and at Yale University.

“I was a radical Democrat, and I believed all this stuff that they believed, including that Republicans were horrible racist people,” he said, to laughs. “And then I started listening to Ronald Reagan.”

The tone shifted sharply at the entrance of Senator Ted Cruz of Texas, who assailed Republican leaders for failing to fight sufficiently for conservative causes.

“We have met the enemy, and they is us,” he said, paraphrasing a famous comic strip.

He marveled that, in the era of the Affordable Care Act, Republicans had managed in 2012 to nominate a candidate, Mitt Romney, who had overseen similar efforts as governor of Massachusetts.

“Literally there are 7 billion people on the face of planet Earth,” he said, suggesting the party would have been better off approaching one of them at random.

Mr. Cruz accused many Republicans in Washington of seeking to become “bosom buddies” with their peers, though he stumbled over the line, emitting something resembling “boosy buttoms.”

The crowd laughed.

“Freud’s going to have a field day with that,” he said.