“It will be a woman – a very talented, very brilliant woman,” Trump said at the rally in Fayetteville. “We haven’t chosen yet, but we have numerous women on the list.”
Amy Coney Barrett, whom Trump previously appointed to the US Court of Appeals for the Seventh Circuit, is seen as the front-runner for the spot.
Barrett is a devout Catholic who has criticised the 1973 Roe vs Wade decision that legalised abortion across the US. She is only 48 years old – a factor that makes her especially appealing for conservatives given Supreme Court justices have lifetime terms.
Trump is also reportedly considering Barbara Lagoa, a Hispanic judge from Florida, and Allison Jones Rushing, who is in her late 30s.
Republican Senator Susan Collins – a moderate who is facing a tough re-election fight in her state of Maine – said that whoever wins the presidential election should nominate Ginsburg’s replacement.
Democrats would have to convince another three Republicans to join Collins to stop Republicans filling Ginsburg’s seat on the nation’s most powerful court by the end of the year.
The death of Ginsburg, a progressive icon who played a crucial role in the development of laws against sex discrimination in the US, has led to an outpouring of grief among Democrats and prompted a surge of donations to the party.
Democrats have accused Republicans of hypocrisy given they blocked Barack Obama from attempting fill a vacant Supreme Court seat in 2016 because it was an election year.
ActBlue – a website that helps Democratic candidates, committees and organisations raise money – reported processing donations worth nearly US$57 million ($78 million) in the half-day following the announcement Ginsburg’s death.
In a video to Instagram followers, New York congresswoman Alexandria Ocasio-Cortez pleaded with young voters to show up on November 3 rather than feel demoralised by Ginsburg’s death.
“November is about survival,” Ocasio-Cortez said. “Voting for Joe Biden is no longer about whether you agree with him. It’s a vote to let our democracy live another day.”
Some Democrats are already threatening radical steps – such as expanding the number of Supreme Court judges – if Republicans fill the seat this year. There have traditionally been nine judges on the Supreme court, but this can be changed.
“If Mitch McConnell and Donald Trump ram through someone from Trump’s horrifying shortlist during this legislative session, the next Congress must respond by expanding the Supreme Court,” Mondaire Jones, the Democratic candidate for a safe House of Representatives seat in New York, said in a statement.
“We must expand the Supreme Court to 13 seats, and allow President Biden to fill those vacancies.”
Matthew Knott is North America correspondent for The Sydney Morning Herald and The Age.