Haley continues to face blowback over her proposed requirement that every person on social media be verified by their name and banned from posting anonymously -- a position she later walked back slightly.

"She should come nowhere near the levers of power, let alone the White House," Ramaswamy said, calling the position "fascism."

Haley responded, "What I said was that social media companies need to show us their algorithms."

"I also said there are millions of bots on social media right now," she continued. "They're foreign, they're Chinese, they're Iranian. I will always fight for freedom of speech for Americans. We do not need freedom of speech for Russians and Iranians and Hamas. We need social media companies to go and fight back on all of these bots that are happening."

DeSantis pushed back on her characterization of her past comments.

"You can roll the tape, she said, 'I want your name' and that was going to be one of the first thing she did in office," the Florida governor said. "She got real serious blowback and understandably so, because it'd be a massive expansion of government."

-ABC News' Alexandra Hutzler

“I would absolutely -- absolutely, if they had a plan which showed me, we could get them out safely, you’re damn right I’d send the American Army in there to get our people home and get them home now,” Christie said. The former New Jersey governor accused DeSantis of avoiding the question about deploying U.S. troops to rescue hostages in the Israel-Hamas war after Hamas' terror attack.

-ABC News’ Chris Boccia

What happens when someone rises in the polls? They attract attacks from their opponents. Both DeSantis and Ramaswamy have gone after Haley from the get-go in this debate, putting Haley on the defensive. This isn't really a shock, though, because Haley's poll numbers have been on an upward trajectory, both nationally and in the early states. She also just earned a major endorsement from Americans for Prosperity, a conservative advocacy group, which Haley mentioned when answering about her electability.

Past presidential primary debates have numerous examples of rising candidates facing attacks, but a famous debate from the 2016 Republican nomination race nicely showcases this. Florida Sen. Marco Rubio finished a strong third in the Iowa caucuses, and his campaign looked positioned to potentially compete for another solid finish in New Hampshire. But in the debate just ahead of that primary, Christie hit Rubio hard, most notably when he homed in on a moment when Rubio seemed to repeat a canned line multiple times and started calling the Floridian "Robot Rubio." Rubio finished fifth in New Hampshire and never recovered.

--Analysis by Geoffrey Skelley, 538

DeSantis said Haley opposed Florida’s ban on gender-affirming care, saying she thought “it’s fine and the law shouldn’t get involved with it.” She doesn’t think it’s “fine.” In a June interview on “CBS Mornings,” Haley said “the law should stay out of it” but it should be up to parents until the child is 18. In the interview, Haley said children should “make more of a permanent change” after they turn 18.

During the debate, Haley likened her position on gender-affirming care for minors to age requirements for getting a tattoo: “I said that if you have to be 18 to get a tattoo, you should have to be 18 to have anything done to change your gender.” We’ve heard that comparison before. For what it’s worth, two-third of U.S. states allow minors to get tattoos if their parents consent. And medical experts have told us gender-affirming care is in many cases considered medically necessary, while tattoos are cosmetic.

-Analysis by Katie Sanders of PolitiFact

At the beginning of the year, DeSantis was the clear runner-up in the Republican presidential primary field: He was averaging above 30% in national polls, only about 10 points behind Trump. But DeSantis’ star has fallen the more voters have gotten to know him, it seems, and another candidate is now on the verge of overtaking him as the most viable Trump alternative: Haley.

As of Tuesday, Haley was at 11% in 538’s national polling average of the Republican primary -- just 2 points behind DeSantis for second place. And she’s doing even better in early primary states. She’s polling at 15% in Iowa, and she’s comfortably in second place in New Hampshire (19%) and South Carolina (21%).

She also recently secured the endorsement of Americans for Prosperity Action, a conservative group affiliated with Republican megadonor Charles Koch that is known for its sophisticated political operation.

Why has Haley been on the upswing? The simplest explanation is these debates. On the day of the first debate, she was averaging just 3% in national polls. But according to a 538/Washington Post/Ipsos poll conducted both before and after that debate, Republicans who watched said Haley was one of the strongest performers, and the share who said they were considering voting for her shot up by 17 points.

Republican debate watchers also rated Haley as the second-best performer in the second debate and the strongest performer in the third debate. Probably not by coincidence, her polling numbers have been steadily increasing ever since.

Of course, Haley fans shouldn’t get too giddy. She (and DeSantis) are still far behind Trump both nationally and in the early primary states. Even if Haley does overtake DeSantis and winds up being the last non-Trump Republican standing in the primary, it won’t matter if Trump is winning every state by double digits.

-Analysis by Nathaniel Rakich of 538