If Dick Cheney is anything to go by, it's the VP that has all the power.
The power is in influence, and in leadership. If the house and senate are on the same side as the president then he will have free reign to do whatever he wants.
In many people's minds though, the issue is of the reputation of the office of the president. This is supposed to be the leader of the free world, someone to give moral and ethical leadership to the world, and to move forward the ideals of democracy and integrity. Someone for children to look up to and to aspire to.
Neither candidate in the current election gives us this ideal, but only one will make the US look like the underbelly of Las Vegas.