Justice Ginsburg was appointed to the court by President Bill Clinton in 1993. Originally from New York, she speaks with a hint of a Brooklyn accent and once described herself as “this little tiny little woman.”

The justice, who is known for her lifetime of work fighting for women’s rights, was the subject of a documentary over the summer, and Hollywood is making a movie from her life story. She gained social media popularity in recent years with her own meme and nickname, “Notorious R.B.G.” As the news about Justice Ginsburg spread on social media on Thursday, some Twitter users volunteered to donate their ribs to her, and others called for protective bubble wrap to be sent her way.

During the Obama administration, Professor Chemerinsky and other liberals called for Justice Ginsburg to step down sometime during the summer before the 2014 midterm elections so that Mr. Obama could name her successor. The Democrats went on to cede control of the Senate — and thus the ability to confirm Supreme Court justices — in those elections.

When Justice Antonin Scalia died in 2016, Mr. Obama nominated a centrist appellate judge, Merrick B. Garland, who had been praised by both parties, to replace him. But the Republican-led Senate refused to consider his nomination so that a new president could make the decision. Mr. Trump chose Neil M. Gorsuch to replace Justice Scalia, preserving the court’s 5-to-4 split between conservatives and liberals.

In an interview in 2013, Justice Ginsburg said that she would not base her retirement plans on who was currently in the Oval Office. She said she would stay put “as long as I can do the job full steam, and that, at my age, is not predictable.”

Earlier this year, Justice Anthony M. Kennedy, 81, announced his retirement. He had been a critical swing vote, generally voting with the court’s conservatives but at times embracing liberal views in major cases.

Mr. Trump and Republican allies had hoped Justice Kennedy would step down so that a more conservative justice could be put in place while Senate Republicans were in the majority. Justice Kennedy was replaced by Justice Kavanaugh, one of his former clerks. The Kavanaugh nomination proceedings were the most contentious in decades, and the justice was confirmed in the closest Senate vote since the 19th century.

A hospital spokeswoman on Thursday directed questions about Justice Ginsburg’s condition to the Supreme Court’s press office.