WASHINGTON — For the White House, President Trump’s first nomination to the Supreme Court is partly about getting the chance to make a second.

In tapping Judge Neil M. Gorsuch for an open seat, Mr. Trump chose a candidate with the potential to reassure Justice Anthony M. Kennedy, the swing vote who holds the balance of power on the court, that it would be safe to retire.

The idea is to show Justice Kennedy, 80, that should he step down at some point, Mr. Trump would select as his replacement a nominee similar to Judge Gorsuch, and not one so inflammatory or outside the mainstream as to be unacceptable to Justice Kennedy. Although certainly more conservative than the justice, Judge Gorsuch once clerked for him and has his enduring respect.

Whether that White House strategy would work remains unclear. Several former clerks to Justice Kennedy said on Tuesday that they doubted it would be the decisive factor for him. But it is clear that Justice Kennedy’s status over the next four years holds enormous consequences for the future of the court. While he has shown signs of thinking about retirement, he also cares deeply about the legacy he will leave behind.

The White House is not the only player engaged in the long game with this nomination. Senate Democrats now must decide how far they are willing to go in opposing Judge Gorsuch, particularly after Senate Republicans refused to even give a hearing to President Barack Obama’s last Supreme Court nominee, Judge Merrick B. Garland.

Since Judge Gorsuch will be replacing Justice Antonin Scalia, the conservative anchor on the court who died last February, his confirmation presumably would not alter the ideological division. But Democrats signaled on Tuesday night that they would filibuster him rather than save that option for the next, presumably more significant nomination, as some liberals had quietly urged.

“Everyone involved in the process — the president, the Senate Republicans, the Senate Democrats — needs to fight this nomination with one eye on Justice Kennedy,” said Ron Klain, a former senior White House aide who shepherded court appointees for Mr. Obama and President Bill Clinton. “His decision to retire or remain determines the balance of power on the Supreme Court.”

Where Neil Gorsuch Would Fit on the Supreme Court

Where Trump’s nominee falls on the court’s ideological spectrum.

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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.

He wrote the Obergefell v. Hodges decision that established a constitutional right to same-sex marriage across the nation — a case that he and other legal scholars believe will mark his place in the history books. Some refer to the current bench as the Kennedy court because of his influence, which is all the more reason that conservatives have been eager to replace him.

Justice Kennedy has been silent about his plans, but it was widely noticed by his fellow justices and other court watchers last fall that he had not hired a full complement of clerks for the next term. Some thought he was slowing down when he did not teach last summer in Salzburg, Austria, as he has for many years. Another sign was his decision to schedule his reunion of clerks, normally held every five years, one year early.

But after Mr. Trump’s election, Justice Kennedy moved ahead with hiring clerks and authorized the court spokeswoman to issue a statement meant to dispute speculation that he might retire. The statement said that he had not gone to Salzburg because of conflicting family plans but would return there in 2017, and that the clerks had wanted to hold the reunion early to celebrate his 80th birthday.

Although Judge Gorsuch is closer to Justice Scalia in terms of judicial philosophy, Justice Kennedy admires his intelligence and temperament, former clerks said, enough that he flew to Denver to preside over his swearing-in after President George W. Bush appointed him to the Court of Appeals for the 10th Circuit.

Judge Gorsuch returns the affection. At Tuesday night’s White House ceremony, he noted that he had clerked for both Justice Kennedy and Justice Byron White. “Justice Kennedy was incredibly welcoming and gracious, and like Justice White he taught me so much,” he said. “I am forever grateful.”

Senate Democrats, however, found plenty of reasons to object to Judge Gorsuch, and liberal groups plan to wage a vigorous campaign against his confirmation. Senator Chuck Schumer, the minority leader, said on Tuesday night that he would insist that Judge Gorsuch be approved by the 60 votes necessary to break a filibuster rather than a simple majority of 51.

It is unusual to filibuster a Supreme Court nominee, but it has been tried. When Democrats were in charge of the Senate, they made it impossible to filibuster lower court nominees but not Supreme Court candidates.

If Democrats filibuster Judge Gorsuch, Senate Republicans could eliminate the filibuster for Supreme Court fights, too, making the tactic unavailable for the next nomination. Mr. Trump has already urged Senate Republicans to do so.

Few imagine that Justice Kennedy finds the idea of being replaced by a Trump nominee appealing. “It’s hard for me to believe that an old-fashioned gentleman like Justice Kennedy would be impressed with Donald Trump’s vulgarity and the way he behaves,” said Daniel Epps, a former clerk for Justice Kennedy who now teaches law at Washington University in St. Louis.

Like other clerks, who declined to be identified, Mr. Epps said he thought the justice was unlikely to be swayed by a nominee named by Mr. Trump. If the president had picked someone who genuinely offended him, Justice Kennedy might resolve to stick around longer, but neither Judge Gorsuch nor the other finalist would qualify, they said.

“It’s not a crazy theory, but my sense of Justice Kennedy and Supreme Court justices generally is that the decision of when to leave is very personal and it turns more on what’s happening with them,” Mr. Epps said.

Orin Kerr, another former clerk teaching law at George Washington University, likewise said he did not think the justice would figure Mr. Trump’s plans into his. “Just my hunch, I tend to doubt AMK would make that kind of calculation,” he wrote on Twitter.

But that did not stop even the justice’s own circle from speculating. As Mr. Epps put it, “I am just as curious as you are and the rest of the world.”