Mr. Trump’s strategists understand that filling Justice Scalia’s seat is not as significant as replacing Justice Kennedy. “I’m sure they would dearly love to see him step down soon,” said Walter Dellinger, a former acting solicitor general. “But he would like to be replaced by a moderate. If they chose a firebrand for the Scalia seat, Justice Kennedy might be more reluctant to leave. Of course, there is no guarantee the next nominee will be like this one.”

White House officials, naturally, did not voice that goal publicly. But as he left the announcement on Tuesday night, Senator Orrin Hatch, Republican of Utah, said he believed that Judge Gorsuch’s nomination would reassure Justice Kennedy that the future of the court was in good hands.

“I think Justice Kennedy will really enjoy serving with him, because he knows him well,” Mr. Hatch said, adding, “He might feel like it’s time to retire, too, because he’s talked about that a few times.”

Appointed by President Ronald Reagan in 1988 after two choices were rejected or withdrew, Justice Kennedy has emerged as the pivotal voice on many critical issues over the past three decades. While voting with the conservative wing on economic issues like Mr. Obama’s health care program, he has sided with the liberals on social issues like abortion and gay rights.