They said tens of thousands showed up at what turned out to be 438 #CountonUs marches across all 50 states.
Demonstrators at the Women's March said they were angry that Republicans appear ready to confirm Barrett's nomination so close to Election Day after refusing to move forward Merrick Garland, the pick of former President Barack Obama, a Democrat, more than six months ahead of the 2016 election.
Rachel O'Leary Carmona, executive director of the Women's March, talked about the power of women to end Trump's presidency on the rally. "Trump's presidency began with women taking to the streets, and that's how it's going to end".
The organization, with the help of demonstrators, also plans on sending over five million text messages, asking female voters to take action in the upcoming election.
Despite several Republicans previously saying they would not replace a Supreme Court justice during a presidential election year - and Ginburg's dying wish to be replaced after a new president was elected - Trump nominated Judge Amy Coney Barrett. The Senate Judiciary Committee is expected to vote on Barrett's confirmation on October 22. "Donald Trump is leaving office, and there is no choice for him", she said.
Biden said he is "not a fan" of court-packing, which is a contentious idea because the number of Supreme Court justices has been fixed by law at nine for more than a century.
Protesters - including some dressed as characters from popular television series The Handmaid's Tale, based on a book by Margaret Atwood - marched towards the US Supreme Court.
Jade Tisdol from Boston takes part in the Women's March in Washington D.C. on Saturday. Carol Guzy for NPR
"We Dissent", said a cardboard sign carried by a young woman wearing a red mask with small portraits of Justice Ginsburg.
Mask-wearing protesters marched in Chicago with the same message, banging drums and chanting for Trump's defeat.
"We Dissent", said a cardboard sign carried by a young woman wearing a red mask with small portraits of the liberal Supreme Court justice whose September 18 death sparked the rush by Republicans to replace her with a conservative.
Next month's presidential contest was also the focus of a separate NY protest Saturday in which hundreds of demonstrators protested the killings of Black people by police officers.
SIWWM March for Breonna Taylor: Snug Harbor to Tompkinsville Park at 10 a.m.
"People need to get out and vote", Palmer told those at the event. "Protesting is good but if we don't take it to the polls we're really not going to make the change we want and need".