How committed should a person be with a given government when asked to take part in it?
It seems logical for a president to ask for commitment when he or she is asking some person to work for the government. I imagine, every president asks the chosen person whether he or she wants to join the government in a given position and has the necessary commitment. This is especially true when people join the cabinet. At the cabinet level, people are asked to join the president's team, and therefore they have to be somewhat in-line with what the president is or wants to do. Unless, of course, the president (if he is clever) specifically asks for constructive criticism. Nonetheless, a certain level of commitment should be there. If not before he or she takes up the post, at least after the post is taken. As said before, the person is joining the president's team and therefore he or she has to do what the president "orders" to do. There is not much choice.
But, where does that commitment end or should end?