A majority of voters believe the winner of the next election should fill the Supreme Court vacancy left by the death of Ruth Bader Ginsburg, a new poll from the New York Times and Siena College finds.

Why it matters: President Trump and Senate Republicans have vowed to swiftly confirm his nominee Amy Coney Barrett, in part hoping for a political boost as the conservative base is extremely motivated by issues concerning the court. The poll indicates that moving fast may not help them with voters they also need to win over: women, independents, and college-educated white voters.

Driving the news: Trump said in an interview with "Fox & Friends" on Sunday that he believes the Senate will "easily" confirm Barrett for the election, and insisted that Democrats would do the same if they were in the GOP's position.

• Senate Judiciary Chairman Lindsey Graham said Saturday he expects confirmation hearings to start Oct. 12 and for his committee to approve her by Oct. 26.

Details: 56% of likely voters said they wanted the winner of the November election to pick the next Supreme Court justice, compared with just 41% who thought Trump should nominate someone before the election. Trump nominated Amy Coney Barrett on Saturday.

• The gender gap is wide: 62% of women say the opening should be filled by the next president.
• The poll also asked about the right to an abortion, as Barrett, should she be confirmed, is seen as the likely vote to tip the court to overturn Roe v. Wade. 60% of respondents said abortion should remain legal in all or most cases.
• Only 33% of the country believes abortion should be illegal in all cases. "The poll suggests that Mr. Trump would reap little political benefit from a clash over abortion rights: 56% said they would be less likely to vote for Mr. Trump if his justice would help overturn Roe v. Wade, while just 24% said they would be more inclined to vote for him," the Times writes.

The big picture: Biden is leading Trump nationally in voter preference, 49% to 41%, according to the NYT/Siena poll. A second poll out Sunday from the Washington Post and ABC News found Biden is leading Trump 54% to 44% nationally.

Methodology: The NYT/Siena poll was taken the week before Trump nominated Coney Barrett, and is based on interviews with 950 voters with a margin of error of 3.5%.