For years, he has infuriated conservatives with decisions striking down prayer at public school graduations and upholding abortion rights - and exasperated liberals with decisions on affirmative action and campaign finance laws.
McConnell changed rules for filibusters on Supreme Court justices previous year to overcome Democratic opposition and confirm Trump's first appointment, Justice Neil Gorsuch. The search, the president said, will begin immediately, and Kennedy's replacement will be chosen from the list of 25 candidates he considered previous year, when he ultimately chose Gorsuch.
"This will be one of the great constitutional fights of the country's history", Waldman said.
Republicans now hold a bare 51-49 majority in the Senate, although that includes the ailing Sen.
"This fall, we will vote to confirm Justice Kennedy's successor".
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Regardless of who replaces him, Kennedy's departure will be a massive change for the high court, where he has been the crucial swing vote for more than a decade. The last thing the large group of Democratic senators running in pro-Trump states need right now is a vote that could either infuriate the GOP's right-to-life base or discourage anti-Trump Democratic voters.
"I expect the nominee to be like Justice Gorsuch, to demonstrate excellence in every respect, and to earn widespread support from the American people, and bipartisan support for confirmation in the Senate", Leo said.
Kennedy was nominated in 1987 by President Reagan to the court, after Robert Bork's nomination failed and Douglas Ginsburg was pressured to withdraw after questions were raised about his admission he had smoked marijuana several times. "Anthony Kennedy kept the court up to date with where society was moving".
Cruz was responding to Senate Minority Leader Chuck Schumer's call for the "Biden rule" to be used, which would delay a nomination until after the November midterm elections.
The other two older justices, Ruth Bader Ginsburg, 85, and Stephen Breyer, 79, are Democratic appointees who would not appear to be going anywhere during a Trump administration if they can help it.