Backstay, never bought a suit, never went to Vegas
The important thing here is the separation of state and government. It is important that the head of government is not omnipotent and there are methods by which problems with the head of government can be dealt with by the head of state. If there is an indication that the head of government is unable to run a decent government (doesn't just mean popular), the parliament and senate can indicate this and the head of state inform the head of government that the head of government must stand aside and a new head of government must be put forth. This does not mean that the vote of the people is ignored, just that the "first among equals" as signified by the ability of the parliament and senate to agree to his/her leadership must stand aside. It is a lot easier if there are more than one political party involved. I don't know how the US got involved with only two parties, but it would be nice to see even a small third party emerge from either end of the political spectrum.
Every time we have a third party it robs the election from one or the other of the two primary parties. Also known as "wasted votes".