Gov. Scott Walker of Wisconsin with Trump on Thursday night during a break in the first prime-time Republican presidential debate for 2016. AP Despite a critically shaky debate performance and a fresh round of controversy, real-estate magnate Donald Trump still leads the Republican presidential field, according to several new polls.

A new poll from NBC and SurveyMonkey showed Trump's popularity among GOP primary voters mostly unchanged. According to the new poll, 23% of Republican-primary voters said Trump would be their first choice for president if the election were held today. That's up from 22% last week, though well within the poll's 3.4% margin of error.

On Monday, the firm Morning Consult released a poll that showed Trump's support nationally increasing to 32% from 25% last week. Reuters released a national survey that found Trump holding steady, meanwhile, though the poll had a noticeably large 6.7% margin of error.

And Public Policy Polling also released a poll of Iowa that showed Trump leading among Republican primary voters in the Hawkeye State, with 19%. That was 7 points ahead of the next candidate, retired neurosurgeon Ben Carson.

“Donald Trump’s public fight with Fox News might hurt him in the long run,” Dean Debnam, President of Public Policy Polling, said in a press release. “But for the time being he continues to lead the pack.”

All three polls were conducted after Thursday, the night of the first Republican debate of the 2016 election.

The polls also showed some big winners from the prime-time debate — which featured the 10 most popular GOP candidates in the polls — and the lower-tier debate, which featured the other seven candidates. NBC/SurveyMonkey reported former Hewlett-Packard CEO Carly Fiorina jumped to 8% from 2% after what many pundits and analysts said was the strongest performance of the early debate.

Morning Consult showed her up 3% from 1% the week before, and also showed Fiorina's favorability ratings jumping significantly.

Republican presidential candidate Carly Fiorina speaks at the RedState Gathering, Friday, Aug. 7, 2015, in Atlanta. AP Photo/David Goldman

Another interesting finding is a surge in popularity for Sen. Ted Cruz of Texas. While almost every candidate besides Fiorina remained virtually unchanged considering the margin of error, Cruz shot up to 13% from 6% in the NBC/SurveyMonkey poll.

The poll showed a surge in popularity that corresponds with what many respondents saw as a strong debate performance: Aside from Fiorina and Sen. Marco Rubio of Florida, Republican primary voters said Cruz performed best at the debate.

Morning Consult, however, found that Cruz's support had dropped within the margin-of-error, so it's unclear whether NBC/SurveyMonkey's poll is an outlier.

Many political pundits on both sides of the spectrum have said Trump's supposedly poor debate performance, as well his subsequent tangling with Fox News host Megyn Kelly, would most likely result in a drop in popularity.

The new polls don't show that effect — yet. But it's unclear whether Trump will remain at the same levels after his widely condemned comments about Kelly on Friday, when he made a remark that critics interpreted as lewd and sexist.

Morning Consult's Reid Wilson, however, wrote that Trump's "support shows no evidence of slipping after he told a CNN anchor on Friday night that Kelly, one of three moderators overseeing the Fox News debate, had 'blood coming out of her eyes. Blood coming out of her wherever.'"

The polls were mostly conducted on Friday and Saturday, meaning many voters may not have been fully aware of those comments when responding to the poll.

It's also worth noting that some political analysts remain skeptical of the NBC/SurveyMonkey poll results. After airing the results on Sunday's "Meet The Press," host Chuck Todd took to Twitter to defend the methodology.

NBC/SurveyMonkey and Morning Consult both conducted their polls online. Experts have been wary of online poll results for years, partially because some believe that respondents tend to skew younger, and pollsters have found it difficult to find representative samples of a population when conducting polls online.

But since jumping into the polling business, SurveyMonkey has established itself as a reliable polling source. Jon Cohen, the vice president of survey research at SurveyMonkey, noted on Twitter that SurveyMonkey polls correctly predicted the outcome of the 2014 midterms, as well as the outcomes of the recent United Kingdom parliamentary elections — both of which other polling organizations missed badly.

This post has been updated to include the PPP, Morning Consult polls.