Democrats close to Ms. Harris said she wanted to carefully consider the potential impact of her endorsement; was mindful that two of her female colleagues, Senators Amy Klobuchar of Minnesota and Elizabeth Warren of Massachusetts, were still in the race; and was uneasy about the prospect of backing a candidate only to see him or her lose California.

Mr. Biden has lavished praise on Ms. Harris since she departed the race, predicting she would have a wealth of political opportunities in the future. And when asked directly if he would consider her as his running mate, he said, “Of course I would.”

A Biden-Harris rapprochement would represent an extraordinary turnaround in their relationship after she so memorably confronted him on the debate stage last summer. Yet their would-be alliance is less surprising on closer inspection.