When Justice Ruth Bader Ginsburg joined President Barack Obama for lunch in his private dining room in July 2013, the White House sought to keep the event quiet — the meeting called for discretion.

Mr. Obama had asked his White House counsel, Kathryn Ruemmler, to set up the lunch so he could build a closer rapport with the justice, according to two people briefed on the conversation. Treading cautiously, he did not directly bring up the subject of retirement to Justice Ginsburg, at 80 the Supreme Court’s oldest member and a two-time cancer patient.

He did, however, raise the looming 2014 midterm elections and how Democrats might lose control of the Senate. Implicit in that conversation was the concern motivating his lunch invitation — the possibility that if the Senate flipped, he would lose a chance to appoint a younger, liberal judge who could hold on to the seat for decades.

But the effort did not work, just as an earlier attempt by Senator Patrick Leahy, the Vermont Democrat who was then Judiciary Committee chairman, had failed. Justice Ginsburg left Mr. Obama with the clear impression that she was committed to continuing her work on the court, according to those briefed.

In an interview a year later, Justice Ginsburg deflected questions about the purpose of the lunch. Pressed on what Mr. Obama might think about her potential retirement, she said only, “I think he would agree with me that it’s a question for my own good judgment.”

With Justice Ginsburg’s death last week, Democrats are in a major political battle, as Republicans race to fill her seat and cement the court’s conservative tilt.

Mr. Obama clearly felt compelled to try to avoid just such a scenario, but the art of maneuvering justices off the court is politically delicate and psychologically complicated. They have lifetime appointments and enjoy tremendous power and status, which can be difficult to give up.

Still, presidents throughout American history have strategized to influence the timing of justices’ exits to suit various White House priorities.