Battle already brewing over Trump's next Supreme Court pick

Battle over the Supreme Court

WASHINGTON -- Senate Democrats joined protesters outside the Supreme Court on Thursday, vowing to block the president's nominee for the Supreme Court after Justice Anthony Kennedy announced his retirement a day earlier.

"Women's access to safe, legal abortions on the line," said Sen. Elizabeth Warren.

They tried to push the Senate Majority Leader Mitch McConnell to delay a vote on the nominee, the way he held up and eventually sunk President Barack Obama's pick, Merrick Garland.

"Is Sen. McConnell prepared to keep this office vacant until after the election? I hope so," said Sen. Dick Durbin.

That hope was quickly dashed, as McConnell said that the Senate will vote to confirm Kennedy's successor this fall. Because he changed Senate rules last year, Supreme Court nominees can now be confirmed by a simple majority.

Republicans expect the president to nominate a strong conservative along the lines of his first pick, Neil Gorsuch. Leonard Leo of the Federalist Society helped to craft the president's list of potential picks. On "CBS This Morning," he downplayed the threat to abortion rights.

"I don't think people should be worried about Roe v. Wade or any other particular case," he said.

But the vote could hinge on two moderate, pro-abortion rights Republicans. Maine's Susan Collins and Alaska's Lisa Murkowski. Collins said Thursday she's looking for a justice who views Roe v. Wade as settled law.

Judicial adviser Leonard Leo on Trump's Supreme Court list
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    Nancy Cordes is CBS News' congressional correspondent.