Trump said shortly after Kennedy's announcement Wednesday he will start the search "immediately" and consult a list of candidates he compiled two years ago, before he was even elected president.
Thomas Hardiman, a judge of the 3rd U.S. Circuit Court of Appeals, was Trump's runner-up to Gorsuch and potentially the front-runner to now succeed Kennedy, who was appointed by former President Ronald Reagan in 1987. In his early 50s, Hardiman is known as a staunch gun rights advocate -- a stance that, given recent high-profile mass shootings, would almost certainly spark a contentious nomination should he receive the nod.
Other favorites to land the nomination include 7th Circuit Court of Appeals judge Amy Coney Barrett, D.C. Circuit Court of Appeals judge Brett Kavanaugh and 6th Circuit Court of Appeals judges Raymond Kethledge and Amul Thapar. Thapar would be the first Indian-American to sit on the high court bench.
The candidates recently added to Trump's list include Barrett, Kavanaugh, Georgia Supreme Court Justice Britt Grant, Kevin Newsom of the 11th Circuit of the U.S. Court of Appeals and Patrick Wyrick of the Oklahoma Supreme Court. Utah Sen. Mike Lee, an attorney who has never been a judge, is also under consideration, although he said in 2016 he wasn't interested in a nomination.
Exactly when Trump's nominee could join the Supreme Court, though, remains a question.
Senate Democrats are pushing to have Kennedy's replacement evaluated in January -- after the November midterms when a new Senate is seated. They say whoever the nominee is shouldn't be considered so close to the midterms -- an argument Republicans used to sink President Barack Obama's nomination of Merrick Garland to replace Scalia in 2016.
Senate Minority Leader Chuck Schumer said this week "the Senate should follow the rule they set in 2016 not to consider a Supreme Court nominee in an election year," and that failing to follow that principle would be the "height of hypocrisy."
Senate Republicans, though, have said they won't wait -- saying the two situations are entirely different.
"That was a presidential election year, so it was very, very different," said Sen. James Lankford, R-Okla. "We're not in a presidential election year. Last time, it was the year that a new president's being elected."
"Why would we do that? I understand with a presidential race, but why would you do it with a Senate race? It's a huge difference," Sen. Bob Corker, R-Tenn., said. "I can understand a presidential race ... but I can't imagine a midterm election affecting that."
Traditionally, Senate Democrats would have been able to stall Trump's nomination. But a rule change by Republicans last year to ensure Gorsuch's confirmation now requires only a simple Senate majority of 51 votes (down from 60) to approve a Supreme Court appointment. With a narrow majority in the Senate, Republicans would be able to confirm any Trump nominee.
Other potential nominees under consideration include Keith Blackwell of the Georgia Supreme Court; Charles Canady of the Florida Supreme Court; Steven Colloton of the 8th Circuit Court of Appeals; Allison Eid of Colorado Supreme Court; Raymond Gruender of the 8th Circuit Court of Appeals; Joan Larsen of the Michigan Supreme Court; Thomas Lee of the Utah Supreme Court; Edward Mansfield of Iowa Supreme Court; Federico Moreno of the U.S. District Court for the Southern District of Florida; William Pryor of the 11th Circuit Court of Appeals; Margaret A. Ryan of the U.S. Court of Appeals for the Armed Forces; David Stras of the Minnesota Supreme Court; Diane Sykes of the 7th Circuit Court of Appeals; Timothy Tymkovich of the 10th Circuit Court of Appeals; Don Willett of the Texas Supreme Court and Robert Young, Chief Justice of the Michigan Supreme Court.