According to the New York Times, several people close to Mr. Biden said on Thursday that they had bowed to growing demands from many anxious members of the party who believed he had come to terms with the idea that he might not win the presidential election in November and might have to drop out of the race. One person close to him warned that the president had not made up his mind to drop out of the race, after three weeks of insisting that there was little to pull him out of the race. But "reality is coming," another said, and it would not be surprising if Mr. Biden soon announced his support for Vice President Kamala Harris to run in his place. Many other Democrats far removed from the White House said there was a growing sense in the party that the president would soon soften.