Democrats said they hoped not to fall into that trap.
“Groups like mine are not planning to go near that issue at all,” said Brian Fallon, the executive director of Demand Justice, which is spending millions on television ads in key states highlighting the consequences of a new justice.
The first ad flight, Mr. Fallon said, will ask why Republicans are rushing through this pick while not addressing the economic fallout of the pandemic.
A clear majority of Americans, 57 percent, said the next justice should be selected by the winner of the November election, compared to only 38 percent who said Mr. Trump and the current Senate should make the appointment, according to a recent Washington Post-ABC News poll. An even greater share of independents and women supported waiting.
Some progressives are pushing Mr. Biden to embrace expanding the Supreme Court if Judge Barrett is confirmed. Mondaire Jones, who is expected to be a freshman House Democrat from New York next year, said he plans to introduce the first legislation to do so, and hoped that Mr. Biden had softened his past opposition.
“Like the rest of the world, waiting to see if he has changed his position,” Mr. Jones said.
Mr. Trump has said he wants a new justice seat in case of an Election Day dispute — “I think this will end up before the Supreme Court,” he said of his battle with Mr. Biden — which has raised alarms for Democrats.
The court has already reshaped the fight for the Senate — at least financially — as Democrats saw a sudden infusion of tens of millions of dollars. ActBlue, which processes donations to Democratic candidates and causes online, brought in $280 million in the week from 8 p.m. on the Friday after Justice Ginsburg passed away to the follow Friday; the proceeding week it had seen $122 million in donations.
In that time, Jaime Harrison, the Democratic challenger to Senator Lindsey Graham, the Senate Judiciary Committee chairman, added $15.9 million to his television reservations, according to Advertising Analytics — more than Mr. Graham had spent on his entire 2014 re-election.