The whole problem in my mind is what I would owe those who voted me in.
You would owe them nothing. You would be in office to serve the interests of the nation, not merely the interests of those who voted for you.
Unless somehow I managed to somehow just magically become president, I would owe my voter base a bunch of promises and also I would have to conform to the image that I presented to the public when they voted me in.
No. You would have made those promises (really, commitments, not promises) to the nation, not just to your voters. So, yes, you would have a moral responsibility to attempt to live up to those commitments. Or course, circumstances may intervene and modify that moral obligation.
Fundamentalism - the anti-American, anti-Christian branch of American Christianity