You know I think a lot of US citizens who are critical of the US president are mistaken about how much power he actually has and, in some cases, jealous of what they perceive to be a position of prestige. While the president certainly has a lot of influence over US policies he is far from an absolute ruler.
Apparently Harry Truman used to refer to the White House as the big white prison. The president's job is not all that dissimilar to the jobs others have. He does not create his own schedule, his schedule is created by a team of people working in the west wing and presented to the president each day. He is essentially required to obey this schedule lock stock and barrel. While I'm sure he can alter the events on this schedule to a certain degree for the most part he is locked into what he is told to do and where he is told to be.
It's not really the people that literally write this schedule that hold him to it, but the others involved in the schedule. If a meeting with republican leaders has been scheduled than the president must obey this for he cannot afford to further upset republican leaders because he needs them in order to further whatever agenda the democratic party desires to push. In this particular case it's not only the republicans that force the president to obey this schedule, but also the democrats.
They say the president, in this case a democrat, is the leader of the democratic party, but that's not really true. The president has the ability to push the democratic agenda and a very limited ability to mold the democratic agenda. Should the president ever step outside the bounds of what democrats consider to be democrat he runs the risk of losing the support of his fellow democrats and essentially being excommunicated from the party. His goals for the nation fall to pieces along with his reputation.
The president is essentially a prisoner held captive by the populace of the United States. The bars that surround the White House not only serve to keep offenders out, but to keep the president in. While it's true he can exit those bars he would be met by an army of cameras ready to plaster his face all over the news for the populace to judge.