No, Mr Obama cannot. Any more than W could. Egypt will decide what it does politically. All the US can do, as it has done in the current uprising, is work with the Egyptian military as a force for moderation and restraint.
Harry Truman retied on a US Army pension of $13,500 a year and he drove his wife back to Missouri in his own car after Eisenhower's inauguration. He turned down fancy job offers, saying "You don't want me, you want the office of the President. That doesn't belong to me, it belongs to the American people and it is not for sale." You can count, on one hand, the politicians in America, the Britain and Egypt who would say the same today.
You've heard of "Disgusted, Tunbridge Wells"? Well, I live in Holland Park and I've Had It. Up to here! An old curmudgeon, I rant and rave about things I read, see or hear in the News. Frequently sarcastic, irreverent and libertarian; often wrong - but never uncertain.