The first question of the night went to DeSantis, who was asked about his stagnating poll numbers and whether voters are telling him "not no but not now."

"So we have a great idea and American voters actually make these decisions, not pundits or pollsters," he responded, adding he's "sick" of hearing about the polls.

"The voters are going to be able to speak and we're going to earn this nomination," he continued. "I am sick of Republicans who are not willing to stand up and fight back against what the left is doing to this country. You've got to be willing to stand strong and you've got to be willing to beat these people."

-ABC News' Alexandra Hutzler

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

Hanging over the Republican presidential primary is the doubt that any candidate can overtake Trump. The former president is polling close to 60% in 538’s national polling average -- a historically strong position. In the modern presidential primary era, which dates back to the 1970s, only three non-incumbents before Trump clearly polled north of 50% nationally around this time: Al Gore in the 2000 Democratic contest, George W. Bush in the 2000 GOP primary and Hillary Clinton in the 2016 Democratic race.

Tellingly, all three went on to win their party's nomination -- although it wasn’t always easy.

But Trump is polling in the mid-40s in Iowa and New Hampshire, which might give DeSantis or Haley an opening. Trump still leads in those states by around 25 points, yet we have seen some sizable past leads disappear by the time voting began. In December 2003, Howard Dean held an edge over of Dick Gephardt in Iowa and led John Kerry by 20 to 30 points in most New Hampshire polls of the Democratic primary. But Dean stumbled to a third-place finish in Iowa, and Kerry ended up winning both states en route to the nomination.

In early December 2007, in the Republican primary, Mitt Romney was running close with Mike Huckabee in Iowa and led John McCain by double-digit margins in New Hampshire. But Huckabee won Iowa, McCain won New Hampshire and then also won South Carolina, putting McCain on course to claim the GOP nomination. And while Bernie Sanders didn’t win Iowa in the 2016 Democratic nominating contest against Clinton, he did nearly tie her there in the caucuses after trailing Clinton by 10 to 20 points in December 2015.

It will still be a tall order to catch Trump, however.

Trump is the first former president in more than 75 years to run again after leaving office, and he maintains clear popularity with a significant portion of the GOP. As a result, many of his supporters say they’re only going to support Trump and aren’t considering alternatives, unlike large swaths of voters in past primaries. This raises Trump’s support floor and lowers the support ceiling for candidates like DeSantis or Haley, who likely need to win over at least some Trump backers to have any chance of winning.

-Analysis by Geoffrey Skelley of 538

Haley and Ramaswamy -- who are both set to be on stage again -- have had multiple fiery exchanges so far in the GOP debates, and Wednesday could see more sparring.

Among their mutual jabs, during the second primary debate, in September, Haley said she felt "a little bit dumber" listening to the entrepreneur.

"TikTok is one of the most dangerous social media apps that we could have. I -- honestly, every time I hear you, I feel a little bit dumber for what you say," Haley said at one point, noting Ramaswamy's recent participation on TikTok despite his criticism of the platform.

Ramaswamy responded that the Republican Party would be better served "if we're not sitting here hurling personal insults and actually have a legitimate debate about policy."

Discussions on the social media platform prompted another notable exchange during the third debate, last month. After Ramaswamy mentioned that Haley's daughter has used TikTok, despite criticism of the Chinese-owned app, Haley lashed out.

"Leave my daughter out of your voice," she said, adding with an eye roll: "You're just scum."

Ramaswamy took another swipe at Haley during the third debate, saying, "Do you want a leader from a different generation who's going to put this country first, or do you want Dick Cheney in three-inch heels?"

Haley responded, "I'd first like to say they're five-inch heels, and I don't wear them unless you can run in them. The second thing that I will say is, I wear heels, they're not for a fashion statement -- they're for ammunition."

-ABC News' Meredith Deliso

Ramaswamy again trained his ire toward Haley, with whom he has feuded across the debates this year, saying she was “woke” and “had a corruption problem.” Ramaswamy raised a notepad which had the message “NIKKI=CORRUPT.” A chorus of boos filled the venue.

The entrepreneur said Haley would “send your kids to die so she can buy a bigger house.”

Given the chance to respond, Haley said only, “No. It’s not worth my time to respond to him.”

- ABC News’ Chris Boccia