Chuck Schumer met with Supreme Court nominee Brett Kavanaugh

Supreme Court nominee Brett M. Kavanaugh tried to woo prominent Democrats on Tuesday on Capitol Hill ahead of his confirmation hearing next month, but the party’s leader vowed to oppose him just minutes before heading into their private meeting.

Senate Minority Leader Charles E. Schumer spent an hour-and-and-a-half with the nominee, probing him about the extent of the president’s authorities, the legality of the Affordable Care Act and abortion rights.

The New York Democrat said Judge Kavanaugh refused to speak about cases that may come before him if he’s confirmed, and wouldn’t say whether a sitting president could be subpoenaed, which could happen if special counsel Robert Mueller tries to compel President Trump to testify in his probe over Russian collusion.

“This has been a traditional dodge of the hard right nominees,” Mr. Schumer said. “Nominees have to be able to answer questions with sufficient substance.”

He said Judge Kavanaugh also refused to hold off on his confirmation hearing until all of his records from his time working in the Bush White House were received by the Senate from the National Archives.

Democrats have tried to slow walk the nomination process by demanding millions of documents from Judge Kavanaugh’s time working as a press secretary for President George W. Bush and in the White House Counsel’s Office before he became a federal appeals court judge.

Republicans, though, have plowed ahead and set a date for Judge Kavanaugh’s confirmation hearing, Sept. 4, declining to request all of the records from his time as Mr. Bush’s secretary. They’ve focused instead on his records from the White House Counsel’s Office.

“This is a publicity stunt. This is trying to delay and distract from his record,” said Carrie Severino, chief counsel of the conservative Judicial Crisis Network, which is backing Judge Kavanaugh.

Meanwhile, other Democrats sat down with President Trump’s nominee Tuesday, including Sens. Kamala Harris of California, Patrick Leahy of Vermont and Claire McCaskill of Missouri.

Sen. John Cornyn, Texas Republican, was optimistic about their meetings.

“They will find him what I found him as — [a] highly qualified person of good character,” Mr. Cornyn said.

Ms. McCaskill is one of several Democrats up for re-election in a state Trump won handily in 2016.

She questioned the president’s nominee about removing dark money from politics as well as health care access, which is a focus for Democrats ahead of the 2018 midterms.

Ms. McCaskill, though, is waiting to hear more from Judge Kavanaugh at his confirmation hearing before revealing how she will vote.

She didn’t back Mr. Trump’s first Supreme Court pick, Justice Neil M. Gorsuch, and her Republican challenger who’s vying for her seat, Josh Hawley, suggested Ms. McCaskill only met with Judge Kavanaugh on Tuesday because Mr. Schumer did.

“I’m glad she got Chuck Schumer’s permission to do so. But the fact is, [Missouri] needs a senator who doesn’t ask permission from the party bosses to represent this state,” Mr. Hawley tweeted.

But Democrats weren’t the only lawmakers Judge Kavanaugh was trying to impress Tuesday. He also sat down with moderate Republican Susan Collins of Maine.

Ms. Collins has said she wouldn’t support a Supreme Court nominee who is hostile to abortion rights.

After the meeting, she told reporters she asked him about Roe v. Wade, the 1973 landmark case that legalized abortion.

“He said that he agreed with what Justice Roberts said at his nomination hearing, in which he said it was settled law. We had a very good, thorough discussion,” Ms. Collins said.

Like Chief Justice John G. Roberts Jr., Justice Gorsuch also acknowledged prior Supreme Court cases dealing with abortion rights were settled law during his confirmation hearing last year.

But Mr. Schumer said that’s not a confident promise that Judge Kavanaugh wouldn’t overrule Roe or subsequent cases protecting women’s reproductive rights if confirmed.

“Saying a case is settled law is not the same thing as saying a case was correctly decided,” Mr. Schumer said.