The question of whether Mr. Mubarak will yield power willingly  and how and under what timetable he might do so  are driving the Obama administration’s national security team to assess and reassess their strategy in dealing with him. It is being watched intently by the antigovernment protesters in Cairo, much of the Arab world and even by members of his own government.

The protesters, along with American and Western officials, are unsure to what degree Mr. Mubarak still calls the shots. There is speculation here and in Cairo that Omar Suleiman, whom Mr. Mubarak named as vice president eight days ago, is in charge now. Since a tense 30-minute phone call between Mr. Obama and Mr. Mubarak last Tuesday night ended with Mr. Mubarak balking at American suggestions that he leave power, most of the Obama administration’s negotiations have been with Mr. Suleiman, according to American officials.

Still, Mr. Suleiman and other Egyptian officials have taken pains to show that their actions are at their boss’s behest, even if he does not appear to be publicly managing the country’s crisis.

American and Egyptian officials say that such considerations are all part of a carefully calibrated process aimed at avoiding a direct challenge to Mr. Mubarak’s unwavering belief that if you make concessions  like tendering a resignation  in the face of pressure, you invite more demands. Concessions must be made on the Mubarak stopwatch, say those who have worked with him. They describe a man who often refuses to accept an idea when it is first presented, but weeks later, embraces it as his own.

Mr. Mubarak, 82, has survived three wars, an Islamic uprising and multiple assassination attempts. Two years ago, an aneurism caused the sudden death of his 12-year-old grandson, Muhammad, a deep personal blow. Through all of that, Egyptian and American officials said, he continues to believe that his country can succeed only if he is at the helm to protect it from being taken over by Islamists (He deplores the Muslim Brotherhood, who he has long believed had a hand in the assassination of his predecessor, Anwar el-Sadat).