WASHINGTON — A clear majority of voters believe the winner of the presidential election should fill the Supreme Court seat left open by the death of Justice Ruth Bader Ginsburg, according to a national poll conducted by The New York Times and Siena College, a sign of the political peril President Donald Trump and Senate Republicans are courting by attempting to rush through an appointment before the end of the campaign.

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

More striking, the voters Trump and endangered Senate Republicans must reclaim to close the gap in the polls are even more opposed to a hasty pick: 62% of women, 63% of independents and 60% 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 Barrett, a fiercely conservative jurist, could offer a pivotal vote should she be confirmed: 60% of those surveyed believe abortion should be legal all or some of the time.

The poll suggests that Trump would reap little political benefit from a clash over abortion rights: 56% said they would be less likely to vote for Trump if his justice would help overturn Roe v. Wade, while just 24% said they would be more inclined to vote for him.

Beyond the coming battle over the court, the survey indicates that Trump remains an unpopular president who has not established a clear upper hand over Joe Biden, the Democratic nominee, on any of the most important issues of the campaign. Voters are rejecting him by wide margins on his management of the coronavirus pandemic, and they express no particular confidence in his handling of public order. While he receives comparatively strong marks on the economy, a majority of voters also say he is at least partly to blame for the economic downturn.

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Perhaps the most comforting news in the poll for Republicans is that at least some Americans appear to have fluid or contradictory opinions on the confirmation process. While most voters would prefer that the next president appoint Ginsburg’s successor, the country was effectively split on whether the Senate should act on Trump’s nomination: 47% of voters said it should, 48% said it should not, and 5% were undecided. Still, women and independents were firmly against the Senate seating Trump’s appointee.

The poll had a margin of sampling error of 3.5 percentage points.

Ginsburg’s death has jolted Washington just weeks before the election, heralding the possibility of an enduring conservative majority on the Supreme Court and marking the latest extraordinary event in perhaps the most unusual election year in modern history.

Yet if the pandemic, economic collapse and increasingly tense racial justice protests have upended life for many Americans, they have done little to reshape a presidential campaign that polls show has been remarkably stable.

Biden is leading Trump, 49% to 41%, the Times survey shows, propelled by his wide advantage among women and Black and Latino voters and by his gains among constituencies that strongly favored the president in 2016, including men and older voters. Biden and Trump are tied among men, with each garnering 45%.

The former vice president appears notably stronger among college-educated white voters than Hillary Clinton did in 2016. Biden is winning 60% of white women with college degrees, compared with 34% for Trump, and he is beating the president among men with college degrees, 50% to 45%. Four years ago, according to exit polls, Clinton won college-educated white women by only 7 percentage points and lost college-educated white men to Trump by 14 points.

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With ballots having already been sent out in a number of states and with the first presidential debate scheduled for Tuesday, Trump has a narrowing window for a comeback.

In an important difference from the 2016 campaign, he would need to draw much closer to 50% to defeat Biden because there is substantially less interest in third-party candidates this year. The Libertarian and Green Party nominees are garnering only 3% combined; that figure is closer to more typical elections than to the one four years ago, when minor-party candidates polled far higher in the period approaching the election and combined to get as much as 6% of the vote in some key states.

With the country so polarized, public opinion on a variety of issues is increasingly linked to presidential preference. The question of which candidate would do a better job picking a Supreme Court justice, for example, effectively matches the White House race: 50% of voters trust Biden on the high court, 43% trust Trump, and 7% are undecided, equaling the percentage of undecided voters in the presidential race.

Voter sentiments are less partisan, though, on the issue of abortion. Although Trump’s vow to quickly fill Ginsburg’s seat has enraged the left, it’s not just liberal intensity that poses a risk to Republicans if the court clash centers on the future of Roe.

The poll shows that 71% of independents said abortion should be legal all or most of the time, and even 31% of Republicans said the same. Only 33% of the country said the procedure should be illegal all or most of the time.

Crucial constituencies said they would be less likely to vote for Trump if his nominee would overturn Roe. That included 65% of independents and 61% of college-educated white voters.

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Dorothy Stanton, 68, of Decatur, Georgia, said she planned to vote for Biden and feared a return to “the days where you couldn’t get a legal abortion.”

“It’s not right that we might be back to those days again,” Stanton said, adding, “If they’re going to put restrictions on a woman’s body, they should put restrictions on a man’s body.”

There is a similar warning sign for Republicans on the issue of health care: 57% of voters, including nearly two-thirds of independents, said they supported the Affordable Care Act, the Obama-era law that Trump’s administration is seeking to overturn in the Supreme Court. Democrats are attempting to put Trump’s challenge to the popular law at the center of the court fight, pairing it with Roe as a measure his nominee might threaten.

About a month after Trump used his convention to castigate Biden and his party in false terms as allies of rioters and criminals, the president is not seen by most voters as a successful law-and-order president: 44% of voters said they approved of his handling of law and order, while 52% said they disapproved.

Trump’s handling of the coronavirus pandemic continues to be a major political liability, and the poll indicates that he has not succeeded in persuading most voters to treat the disease as a quickly receding threat. A majority of voters, 56%, said they disapproved of Trump’s approach to the pandemic, including half of white voters and the same proportion of men, groups that usually lean to the right.

Americans oppose Trump’s policy preferences on the pandemic by significant margins: Two-thirds of voters said they would support a national mask mandate, while 63% said they would support new lockdowns to fight a second wave of the disease if public health experts recommend them. Trump has opposed both measures; he has often ridiculed mask-wearing and has attacked state and local officials for imposing health-based restrictions on public activity.

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Yet 40% of the president’s own party supports a nationwide mask mandate.

Biden has taken an opposing set of positions that is more in line with voters’ preferences. He endorsed a national mask mandate, though he acknowledged a president might not have the power to impose one by fiat, and he has encouraged public officials to implement lockdowns as necessary. He has criticized Trump, who has repeatedly suggested that a vaccine will emerge before Election Day, for politicizing that process.

The poll shows that the president is not making headway with voters by dangling the possibility of a hastily approved vaccine for the coronavirus, as 81% said they would oppose distributing a vaccine before the completion of clinical trials.

And while Trump has insisted that the coronavirus will soon disappear, most voters disagree. Half said they believed the worst effects of the pandemic were still ahead, while 43% said the ugliest phase was over.

The poll shows that Trump is strongest on economic issues, an enduring strength for him: 54% of voters said they approved of his handling of the economy, including about half of women, Hispanics and college-educated white voters — groups that mainly support Biden. The president has staked his reelection in part on the argument that he is best equipped to restore economic prosperity once the pandemic has passed.

But voters’ assessment of Trump’s economic leadership is not entirely positive, and in this area the president appears to be paying a price for his role during the pandemic. Here, 55% of voters said Trump was somewhat or mainly responsible for the economic downturn, compared with 15% who said he was not very responsible for the recession and 28% who said he bore no responsibility at all.

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Much of the electorate appears to be in a pessimistic mood, with a large share of voters convinced that the U.S. government is deeply dysfunctional, and inclined to view the stakes of the 2020 election in drastic terms: 3 in 5 said that the 2020 election would decide whether the United States would remain a prosperous democracy, while only 30% said the country would remain prosperous and democratic no matter who won.

That perspective cut across demographic, regional, generational and ideological lines, with a majority of every subgroup saying that the country’s future as a thriving democracy was at stake.

While a majority of voters — 54% — said that the country’s political system could still address its problems, a full 40% said the U.S. was too divided for the political system to work.

Voters were about evenly split over whether those divisions would ease if Biden was elected president, with about one-third saying the situation would improve and one-third saying it would get worse; 3 in 10 voters said the situation would stay about the same.

But most of the electorate saw little hope for improvement under a second Trump term. Only 17% said the country’s divisions would ease after another Trump victory, compared with 50% who said they would get worse.