SUMMERVILLE, S.C. — There is a notion in South Carolina politics: Voters don’t so much want to see a candidate swing at someone as they want to see how a candidate can take a punch to the nose.

Marco Rubio, Jeb Bush, and Ted Cruz are trying to prove themselves under that standard — and then some. Bloodied and battered in New Hampshire, they are engaged in a vigorous fight in the final days before the state’s Republican primary on Saturday, with voices rising, tempers flaring, and threats of lawsuits flying.

Rubio won a round Wednesday by capturing the coveted endorsement of South Carolina Governor Nikki Haley.

But with Donald Trump maintaining a commanding lead in the polls in a Republican presidential campaign that has gone from negative to just plain nasty, the three-way slugfest for the second- and third-place spots is providing the biggest drama over who can continue — and who will be pressured to drop out — after Saturday’s primary.

Cruz is brawling directly with Trump, with plenty of scars to prove it. Rubio is hammering Bush, trying to keep his rival Floridian’s head under water, even as he woos reporters and cracks rehearsed jokes to disprove his image as a robotic campaigner.

Bush, trying to loosen up, shed his eyeglasses and wore contacts for the first time in his life Wednesday. He is featuring the stars of his dynastic, blue-blood family: his mother, Barbara, is due to visit South Carolina Thursday, on the heels of former president George W. Bush’s appearance with Jeb Bush on Monday.

With each primary state from now on, the pressure on the bottom-tier candidates to quit the race will intensify exponentially. But if either Rubio or Bush emerges from South Carolina as a convincing second alternative to Trump, besides Cruz, that could count as a victory in this topsy-turvey Republican campaign season.

“He(Bush) spent $50 million attacking me,’’ Rubio told reporters on Wednesday. “What I’ve said about Governor Bush is he doesn’t have any foreign policy experience. Which is true. I don’t view that as an attack. I view that as a fact.’’

A few hours later, Bush showed up at a campaign event at a country club. Attendees were ferried on golf carts and Bush spoke overlooking a sun-splashed sixth hole. But he struggled to hide his annoyance — at everything from a faulty microphone to Trump’s ability to dominate the media’s attention to the attacks from Rubio, his one-time understudy.

“It’s hard for me to be lectured to by a gifted young guy who thinks that going to a committee hearing means that you know something about the world,’’ Bush said, his voice rising after ticking off his own resume of living, working, and going on trade missions abroad.

But over the course of nearly an hour, a series of voters — and professed supporters — urged him to be a better campaigner. They like his sobriety, they said, but want Bush to show more vigor, particularly against Trump.

“I was wondering . . . . if you could raise the bar in the next session,’’ one man said.

“The campaign has been co-opted by the P.T. Barnum of our time,’’ another chimed in. “He is getting you off your message, your good message.’’

“I’m the only guy going after him!’’ Bush exclaimed at one point. “I don’t feel like he’s intimidating. He’s a bully.’’

Bush arrived in South Carolina with his campaign aides relieved that he finished in front of Rubio in the New Hampshire primary. They felt that South Carolina provided a place where his family name would finally be an asset, and they are still focused on finishing ahead of Rubio.

But it was Rubio who on Wednesday got a major boost with the endorsement from Haley, who has an 81 percent approval rating among Republicans here.

Haley’s stature has risen over the past year, first after her leadership following the shootings at Emanuel AME Church and then after she directly took Trump on over his proposal to ban Muslims from entering the United States.

The endorsement was as much a blow to Bush as it was a boost to Rubio.

Former president Bush met privately with Haley on Monday afternoon and spoke fondly of her from the stage later that night.

“If she is going to give an endorsement it would be the most powerful, meaningful one in the state,’’ Jeb Bush told NBC News on Tuesday, a day before her support of Rubio became public.

It was the latest shot in the arm for Rubio, who is trying to rebound after a New Hampshire debate where he repeated the same line several times and reinforced complaints that he was a highly scripted candidate.

Since arriving in South Carolina, the once-cloistered Rubio has become more accessible, spending 45-minute sessions with reporters. After each event he lingers, allowing voters to snap photos, lob questions, or even squeeze his dimpled cheeks.

He’s dropping more jokes into his stump speech — including some self-deprecating ones about how he repeats himself.

“I’ve never met her but I’ve paid Sallie Mae a lot of money,’’ Rubio said, referring to his $120,000 in student loans. “That’s a new joke I’ve worked in these last few days. Some people don’t like when I repeat myself, but it’s funny! So I’ll say it.’’

Although Rubio is attempting to be looser during his town-hall-style meetings here, he never lets go of the microphone. Unlike in New Hampshire — and unlike the case with Bush here — there are no questions from the audience.

Trump and Cruz continued escalating their verbal back-and-forth Wednesday with threats of legal action. Trump has said he would sue Cruz if he doesn’t take down ads he says are inaccurate. He has also threatened to file a lawsuit claiming Cruz is ineligible for the presidency because he was born in Canada, to an American mother.

“I have to say to Mr. Trump — you have been threatening frivolous lawsuits for your entire adult life,’’ Cruz said at a press conference. “Even in the annals of frivolous lawsuits, this takes the cake.’’

Cruz, a lawyer who clerked and argued before the Supreme Court, said he would consider deposing Trump himself in court.

“If I want to bring a lawsuit it would be legitimate,’’ Trump said in a statement. “Likewise, if I want to bring the lawsuit regarding Senator Cruz being a natural-born Canadian I will do so. Time will tell, Teddy.’’

In aBloomberg Politics poll released on Wednesday, 36 percent of likely Republican primary voters in South Carolina said they would support Trump, with Cruz a distant second with 17 percent. Rubio was at 15 percent, Bush at 13 percent. Ben Carson was at 9 percent, and Ohio Governor John Kasich at 7 percent.

Bush, in a sarcastic comment at his event, could barely hide his annoyance as he openly indicated he was sick of the polls and punditry.

“It’s all been decided, apparently,’’ Bush said. “The pundits have made it all — it’s all decided. I mean, we don’t have to go vote I guess. It’s all finished. I should stop campaigning maybe, huh?’’

Matt Viser can be reached at matt.viser@globe.com.