Hillary Clinton picked up support over Donald Trump in the presidential campaign, according to a new Wall Street Journal/NBC News poll taken after a videotape of the Republican nominee making vulgar remarks surfaced, but before Sunday night’s debate.

Meanwhile, a plurality of voters reject calls for him to withdraw from the race—which some GOP officials made in the wake of the remarks—and two-thirds of Republicans questioned believe GOP candidates should stand by him as nominee.

According to the new survey, Mrs. Clinton jumped to an 11-point lead over Mr. Trump, 46% to 35%, among likely voters on a ballot including third-party candidates, up from 6 percentage points in September, when the split was 43% to 37% in a four-way contest.

The Wall Street Journal/NBC News survey was taken Saturday and Sunday, in the time between the video being released and his defense of his comments in Sunday’s televised debate with Hillary Clinton. In that debate, Mr. Trump said he had been engaging in “locker room talk’’ and revived accusations of sexual assault by Mrs. Clinton’s husband, former President Bill Clinton.

Interviews for the poll were continuing Monday and could signal whether Mr. Trump had rebounded after Sunday’s debate.