Donald Trump confidently arrived on stage for the start of last week's Republican presidential debate in Cleveland. Those who watched the Thursday night debate were more supportive of Trump than the general public, a new poll found. Getty Images/AFP/Mandel Ngan

WASHINGTON -- Donald Trump doesn’t appear to be suffering from his combative Cleveland debate performance, at least for now, and it may have helped him. The latest post-debate poll of Iowa Republican voters showed Trump was still enjoying a lead in the first caucus state.

Public Policy Polling, a liberal-leaning survey firm that uses automatic polling software and therefore is not likely to be used in determining future debate participants, found Trump placed first with 19 percent of the GOP support in Iowa. For those who watched the debate, he did even better: 21 percent of those who reported watching it live said they support Trump. Trump had a smaller lead among those who watched only news coverage with clips of the debate, and he was in first place with 15 percent but only holding that lead by a single percentage point. He also tied with Wisconsin Gov. Scott Walker among those who didn't watch the debate at all.

After Trump’s Thursday night debate appearance, in which he sparred with Fox News anchor Megyn Kelly and with several of the other candidates, some pundits were eager to bury his campaign. The fight has continued to drag on, with Trump hurling insults at Kelly, including an appearance on CNN during which critics said Trump suggested the Fox News anchor’s menstrual cycle contributed to her attitude toward him. Trump disputed that characterization, saying he was talking about blood coming out Kelly’s eyes and nose.

Donald Trump is leading a Republican primary poll of Iowa after the first GOP debate. Above, Trump with Ohio Gov. John Kasich during a break in the debate Aug. 6, 2015, at the Quicken Loans Arena in Cleveland. Getty Image/AFP/Mandel Ngan

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

Trump continues to struggle with high unfavorable marks. The PPP poll found a sharp divide, with 46 percent giving him favorable marks overall but 40 percent negative. The only candidate with higher unfavorable numbers was New Jersey Gov. Chris Christie, with 44 percent.

Trump also did badly among women. Of those polled, 47 percent had an unfavorable position compared to 36 percent that had a favorable opinion of him. Men, however, were 55 percent favorable opinion and 34 percent unfavorable.

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Still, Trump was managing to pull in enough supporters despite the avalanche of criticism. The poll asked Republicans what quality they were more concerned about in a candidate: electability or ideology. For those most concerned about ideology, Trump was leading 21 percent. For those who care about electability, he was also winning, with 16 percent.

The poll put Walker and Dr. Ben Carson in second place in Iowa with 12 percent of the vote apiece, 7 percentage points behind Trump. Jeb Bush was in fourth place at 11 percent.

Carly Fiorina saw a bump in the polls after her second-string debate performance that was praised as winning the night. She placed fifth at 10 percent, ahead of Texas Sen. Ted Cruz, who polled at 9 percent and Mike Huckabee and Marco Rubio, who were tied at 6 percent. Previous polls by other polling outlets had Fiorina struggling to get above 3 percent and break into the top 10.