The president invited this hype when, in announcing the Kagan appointment, he called her one of America’s “foremost legal minds” and stressed her links to “ordinary people” in fighting against “unscrupulous corporations.” He specifically praised her for, as solicitor general, arguing (unsuccessfully) the government’s side in January in the Citizens United case, in which a narrow court majority opened the floodgates for corporate and special-interest money in federal political campaigns.

Sean Wilentz, a historian who taught Ms. Kagan at Princeton University, said that intellectually, she was reminiscent of the fabled Justice Brandeis. White House advisers and others have lauded the political skills she would bring to the court, citing her ability to work with diverse factions at Harvard Law School — she was tapped for that job by Lawrence H. Summers, then president of the university — and her brokering of an anti-tobacco deal with Senator John McCain, Republican of Arizona, during the administration of President Bill Clinton.

Most everyone who knows Ms. Kagan praises her sharp intellect. Yet her lack of scholarly writings or judicial decisions makes it impossible to call her a towering judicial intellect. As solicitor general, court watchers say, she was only a fairly effective advocate.

She certainly was an effective dean at Harvard, and one empathizes with anyone who has to endure countless faculty meetings. Yet this isn’t the same as negotiating compromises on controversial high court decisions; Daniel Patrick Moynihan, the late New York Democratic senator, was fond of saying that academic politics was so bitter because so little was at stake.

Her role in fashioning the tobacco agreement is exaggerated. Those were the days, 1998, when Mr. McCain was a maverick, and as chairman of the Commerce Committee, eagerly took on the tobacco industry. At the time, David A. Kessler, the head of the Yale University School of Medicine, attributed the success to “John McCain’s courage.”

Ms. Kagan did, as Mr. Obama boasted last week, argue the difficult Citizens United campaign-finance case before the Supreme Court. That was the biggest case she inherited upon taking the job of solicitor general, who usually argues the major cases.

The president insisted that in tapping Ms. Kagan, he had achieved his objective of a justice who identifies with the lives of “ordinary” people. Ms. Kagan has lived almost her entire life in New York; Cambridge, Massachusetts; and Washington.