In a survey of likely voters taken in the week leading up to Mr. Trump’s nomination on Saturday of Judge Amy Coney Barrett to the high court, 56 percent said they preferred to have the election act as a sort of referendum on the vacancy. Only 41 percent said they wanted Mr. Trump to choose a justice before November.

More striking, the voters Mr. Trump and endangered Senate Republicans must reclaim to close the gap in the polls are even more opposed to a hasty pick: 62 percent of women, 63 percent of independents and 60 percent of college-educated white voters said they wanted the winner of the campaign to fill the seat.

The warning signs for Republicans are also stark on the issue of abortion, on which Judge Barrett, a fiercely conservative jurist, could offer a pivotal vote should she be confirmed: 60 percent of those surveyed believe abortion should be legal all or some of the time.