There's one name on the list who is garnering particular attention, however - someone who is reportedly one of four finalists who have already met with Mr Trump in the White House. The senator's office characterized the call as an interview, but the White House would only say the two spoke.
One day after Justice Anthony Kennedy announced his retirement, Demand Justice rallied in front of the Supreme Court.
"I have deep concerns about this nominee", the Democratic senator Chuck Schumer, now minority leader, said at the time.
The future orientation of the Supreme Court depends on who will succeed Kennedy, a conservative. His exit paved the way for Trump to nominate a second justice to the nation's top court.
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We wish his kids, his wife Savannah, his mother Gloria, and LeBron himself nothing but the best in the years and decades ahead. The Cavs played 81 postseason games - one contest shy of an entire regular season - the last four years, winning 55 of them.
As he did with the nomination of Neil Gorsuch as a SCOTUS justice previous year, Mr. Trump is building up anticipation for the announcement, by tweets, public speeches and in interactions with the media.
The public is also split on whether the Court has a partisan lean, with 31% saying it is too conservative, 19% feeling it is too liberal, and 41% believing it is just right.
Trump said during his presidential campaign he'd appoint justices who oppose that decision.
The president has a list of 25 candidates, which he said he has narrowed down to five, including two women. He is not known as a great legal theorist like Kavanaugh, nor is he a "feeder judge" whose law clerks are snapped up by Supreme Court justices. With McCain possibly not able to vote, Trump would need the support of Democrats to win confirmation.
President Donald Trump has spoken with Republican Sen. Harry Reid. The Reid rule requires only a simple majority to confirm a judicial nominee without the threat of indefinite delay through a filibuster.
The social media push is an effort to press the moderate Republican senator to vote against any Supreme Court nominee who would overturn Roe v. Wade, the landmark 1973 case that established a constitutional right to abortion.
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Of course, Anthony infamously told reporters at the end of last season that he would not entertain a role off of the bench. George took the stage at a party in Oklahoma City on Saturday and announced he would be staying with the Thunder.
She also made clear that she "would not support a nominee who demonstrated hostility to Roe v. Wade", on CNN's "State of the Union". That is to say, the legal war will continue, with some encouragement to the handful of Arkansas legislators whose reason for existence is to make it a crime for women to get an abortion.
Walker said that if it comes down to the vice president casting a tie-breaking vote, he thinks it could tear the country apart.
An appointee of President Ronald Reagan, Kennedy was reliably independent, the famous swing vote who at times stood with the four fellow justices appointed by Republican presidents and at others with the four appointed by Democrats.
Appointed by President Ronald Reagan after two nominees failed to be confirmed, Kennedy has always been feted by many liberals for these stands.
Joan Larsen (Pritzker '93) and Diane Sykes (Medill '80) are included on the main list of potential Supreme Court picks. He says both would be threatened by a conservative Trump nominee.
Minuses: Despite a decade on the appeals court, his record is thin in several areas of the law, which worries some conservatives. "No one was asked these questions and as far as I know no one has been asked these questions if they were brought into the process in the White House".
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Pepe headed home from the corner to bring the Selecao back into the match but it was Uruguay who had the last laugh. Santos said his side had studied their opponents but that it was impossible to legislate for Uruguay's first goal.