Following Thursday’s Republican debates, an overnight poll shows Donald Trump maintaining his edge over the crowded field of Republican candidates. The survey also finds a majority of Trump supporters say they would vote for him as an independent candidate for president, in the event he does not win the Republican nomination.

The NBC News online poll conducted by SurveyMonkey over Friday night and into Saturday showed possible movement among the candidates following the debates, as well as Republican primary voters declaring Carly Fiorina the overall debate winner.

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Donald Trump has the support of 23% of Republican primary voters following the debate, which had the highest viewership ever for a primary debate, with 24 million watchers. The poll was in the field for only a 24-hour period, during which Mr. Trump continued to make more headlines for his comments about Fox News moderator Megyn Kelly, which got him disinvited from speaking at a gathering of conservatives in Atlanta.

Ted Cruz and Carly Fiorina were the candidates with the most gains in support, 7 points and 6 points respectively, but there was no real change among most candidates given an error estimate of plus or minus 3.4 percentage points.

Among Trump supporters, a majority – 54% – said they would vote for him for president as an independent candidate, even if he does not win the Republican nomination. During the Republican debate, Trump was met with both boos and cheers from the crowd as he said he would not rule out running as an independent if he didn’t get the Republican nod. About 1 in 5 Trump supporters said they would support the eventual Republican candidate, while about the same number said it would depend.

Among Republican and Republican-leaning voters who watched either of the debates or followed coverage of the debates in the news, Carly Fiorina emerged as the clear winner. Twenty-two percent said Fiorina won or had the best performance in the debate, followed by 18% who said Trump had the best performance. However, another 29% said Trump did the worst in the debate, clearly showing how polarizing he is. When the candidates’ negative performance percentages are subtracted from their positive percentages, Fiorina notched a positive 20, whereas Trump scored a negative 11. Both Marco Rubio and Ted Cruz did well, with net scores of positive 12 and 11. Rand Paul also fared poorly, scoring a negative 11.

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Finally, the poll found that Republican voters report that these debates matter: 25% said a candidate’s debate performance is very important to their vote decision, and another 54% it is somewhat important. The next Republican debate will take place on September 16 at the Reagan Library in California.

The NBC News Online Survey was conducted online by SurveyMonkey from August7-8, 2015 among a national sample of 3,551 adults aged 18 and over. Respondents for this non-probability survey were selected from the nearly three million people who take surveys on the SurveyMonkey platform each day. Results have an error estimate of plus or minus 2.4 percentage points for the entire sample and 3.4 percentage points for Republican primary voters. A full description of our methodology can be found here. The survey was produced by the Analytics Unit of NBC News in conjunction with Penn’s Program on Opinion Research and Election Studies with data collection and tabulation conducted by SurveyMonkey. Analysis by the University of Pennsylvania’s Program on Opinion Research and Election Studies.