"This vacancy should not be filled until we have a new president," Schumer said Friday, carefully echoing the words of Republican Senate majority leader Mitch McConnell in 2016 when he blocked Obama nominee Merrick Garland.
Republicans in theory have the Senate votes to push through a Trump nominee, but could be blocked by only a handful of defections.
Republican Senator Susan Collins became the first to break ranks when she announced Saturday she would not support a vote on any Trump nominee before the election.
The Maine lawmaker is among a handful of moderate Republican senators — including Lisa Murkowski of Alaska — who have already expressed doubts about a rushed vote.
"I totally disagree with her," Trump said of Collins' stance, referring to his 2016 election in adding that "we have an obligation as the winners to pick who we want".
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One prominent Democratic member of the Senate Judiciary Committee, which will oversee the confirmation hearings, is none other than Senator Kamala Harris, Biden's running mate.
Trump has already named scores of conservatives as federal judges, and Democrats fear a deep and lasting shift in balance at the Supreme Court.
"If he's allowed to put more conservatives in, this is going to be disastrous for the next 40 to 50 years," Gloria Browne-Marshall, a civil rights attorney, said on CNN.