"If the nominee is out of the mainstream, we will do our best to keep the seat open," Schumer, D-New York, told CNN's Jake Tapper on "State of the Union" of the Supreme Court vacancy that Trump will get a shot at filling after majority Republicans blocked former President Barack Obama's nominee for a year.
"I'm hopeful that President Trump may nominate someone who is mainstream and could get bipartisan support," Schumer said. "But if they don't, yes, we will fight it tooth and nail, as long as we have to."
Schumer also said he'll oppose eight or nine of Trump's Cabinet nominees, and potentially more.
He specifically said he opposes Alabama Sen. Jeff Sessions, Trump's pick for attorney general, and Oklahoma Attorney General Scott Pruitt, Trump's nominee to helm the Environmental Protection Agency.
"We certainly feel that we have to bring to the American people how different this Cabinet is -- how hard-right, how many conflicts of interest, billionaires," Schumer said.
His comments come the same day Sens. John McCain and Lindsey Graham announced they will vote to confirm Trump's pick for secretary of state, former ExxonMobil CEO Rex Tillerson.
"Listen, this wasn't an easy call. But I also believe that when there's doubt the president, the incoming president, gets the benefit of the doubt, and that's the way I've treated every president that I've had the obligation to vote for or against as a member of the United States Senate," McCain said on ABC's "This Week."
Graham tweeted shortly after: "I will vote to confirm Rex Tillerson as Secretary of State.'
That decision could mean Democrats won't have the votes to stop Tillerson's nomination. Florida Sen. Marco Rubio has also been on the fence, but Democrats would likely have needed all three -- McCain, Graham and Rubio -- to block Tillerson's confirmation.
Democrats alone do not have enough votes to sink any of Trump's nominees, and Schumer noted it will be up to Republican opposition to actually block picks.
Schumer also said he's worried Trump is "using populist rhetoric to cover up a hard-right agenda."
He criticized Trump's actions over his first 36 hours as president, complaining to the CIA of media coverage of the size of his inauguration crowd.
"President Trump is now president. He's not campaigning anymore," Schumer said. "And instead of talking about how many people showed up at his inauguration, he ought to talk about how many people he's going to bring into the middle class."