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In a two-way race, the Democratic presidential nominee earned 52% of support from 500 registered voters surveyed between October 8 to 9.
Trump earned 38% of support.
The poll was the first conducted after the 2005 audio tape leaked of Trump boasting about kissing and groping women. On the tape, Trump said he could "grab" women "by the p---y" because "when you're a star, they let you do it."
Trump apologized for the remarks in a video published just after midnight on Saturday, but many congressional Republicans are worried the comments and Trump's high negatives could put their own races in jeopardy.
An avalanche of prominent Republicans condemned Trump's comments and some, including No. 3 Senate Republican John Thune of South Dakota, have gone as far as to call on the billionaire to step down as the nominee and hand the ticket over to vice presidential nominee Mike Pence.
Trump has refused to obey such calls. Instead, he doubled down during Sunday's debate, going on the offensive by pointing to former President Bill Clinton's history with women.