GREENVILLE, S.C.—When Ruth Silver was watching last week’s Republican debate in her Wantagh, N.Y., living room, she was so impressed with Carly Fiorina’s “class and poise, I wanted to stand up and applaud.”
Ms. Silver, 71 years old, said the former Hewlett-Packard executive’s performance was so strong she began rethinking her support for celebrity businessman Donald Trump.
For now, Ms. Silver is sticking with Mr. Trump but she is part of a shrinking pool: Female voters’ support for the first-time candidate dropped 12 percentage points among likely GOP voters after last week’s CNN debate, according to a CNN/ORC poll conducted Sept. 17-19. The poll has a margin of error of plus or minus 3%.
That decline in support helped drive down Mr. Trump’s standing in the primary field. Although still the front-runner, his backing tumbled by eight percentage points, to 24% from 32% in a CNN/ORC poll conducted Sept. 4-8. Of those who tuned in to watch the debate, 31% of the likely GOP voters said he did the worst job—the highest percentage of any candidate.
Republican front-runner Donald Trump on Thursday declined to refute a questioner who declared that Muslims are a “problem” in America and reiterated the long-debunked rumor that President Barack Obama is a Muslim.
The Trump campaign didn’t respond to requests for comment on Tuesday.
The second debate, which covered both foreign and domestic issues, marked the first flagging of Mr. Trump’s support among GOP voters, an opening that Ms. Fiorina gained from as she shot up to second in the poll at 15%. She also emerged as the clear debate winner, as 52% of likely GOP voters said she did the best job, the poll found.
Mr. Trump took the debate stage after Rolling Stone published disparaging remarks he made in an interview about Fiorina: “Look at that face! Would anyone vote for that? Can you imagine that, the face of our next president?!,” Mr. Trump told the magazine.
In interviews, the celebrity businessman said his comments were misunderstood and he was referring to her persona, not her facial features. Asked about that explanation during the debate, Ms. Fiorina’s rebuttal brought down the house. “I think women all over this country heard very clearly what [Donald] Trump said,” she said.
Mr. Trump’s exchanges with Ms. Fiorina came just weeks after he said Fox News anchor Megyn Kelly had “blood coming out of her whatever” when she asked him tough questions in the first GOP debate, a comment that some interpreted as a reference to her menstrual cycle. Mr. Trump said his remarks were being misinterpreted, and that he wasn’t referring to her cycle.
“I cherish women,” Mr. Trump said on CNN in August. “I want to help women. I’m going to be able to do things for women that no other candidate would be able to do, and it’s very important to me.”
Yet, the personal nature of his remarks are driving away some potential backers and giving even some of his loyalists pause. Mr. Trump’s recent remarks about high-profile women also could hamper a general-election candidacy. In the 2012 election, exit polls showed that 53% of the voters were women, outnumbering their male counterparts.
“I do think he’s a sexist. Absolutely,” said Katie Packer Gage, a Republican strategist who isn’t working for a presidential candidate. “When you talk about the way a woman behaves in the context of their menstrual cycles, it reduces them to something, and suggests they don’t have control of themselves or their emotions.”
Mr. Trump’s financial acumen could be an asset in the White House, said Wanda Owens of Walhalla, S.C., but she has concerns about his ability to handle foreign affairs and his comments about women.
“He’s kind of brutal toward women,” said Ms. Owens, who supports Ben Carson, a retired neurosurgeon and another political newcomer. She added that she questions whether women would be appointed to top positions in a Trump administration.
Mr. Trump’s female backers say they aren’t offended because his blunt rhetoric is just part of his tell-it-like-it-is style.
Joan Belfield in Sayville, N.Y., said the Fiorina comment was “thoughtless,” a “stupid thing to say,” yet she still leans towards Mr. Trump. Is Mr. Trump sexist? Ms. Belfield said no. “He says that about men, too.”
Joyce Kaufman, the host of a popular radio show based in South Florida, also sees the candidate as an equal-opportunity name-caller. “If we want to play with the boys, then we have to play with the boys,” Ms. Kaufman said.
But “wavering” Trump supporter Leeann Frazier of Brownwood, Texas, said she is more concerned about Mr. Trump’s ability to “tone it back” than any specific remarks he has made.
“I don’t take his statements personally as a woman. I don’t think he means that. He just speaks off the cuff, and he’s always been one to go for shock factor and say what he thinks,” Ms. Frazier said.
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