In the era of the Roman Empire, seekers of office would wear the whitest clothing they could find. White has always been a symbol of purity, in this case the purity of truth. Candor was the premium selling point of the day, hence the origin of the word "candidate." Promises and intentions are all any political candidate really has in running, so the forthrightness and dedication in pursuing those promises become the capital of the candidate who is elected to office.
Knowing someone is a promise-keeper is important for obvious reasons: you can only trust someone you know will get the job done. Faith in God is based in knowing that obedience is blessed and sin is punished without variability. Faith in a politician is based on his or her ability to deliver on promises made to the voting public. One easy way to know a politician is not a truthful person is to learn of their marital infidelity.
Who cares what goes on between two consenting adults? Why is someone's personal sex life relevant? It's not that what goes on behind closed doors that's the business of the people, it is the dishonesty and gigantic moral failing of adultery that is meaningful for voters. Whatever David Archuleta's dad did in the back of the massage parlor is meaningless to us; what Senator Ensign of Nevada did proves that he is a liar, unable to keep a central promise in his life. If Sen. Ensign broke the covenant with his wife, whom he presumably loves, what other promises at stake can be tossed away? For all the politicians like Ensign, Larry Craig, Bill Clinton, Gary Hart, Mark Foley and the rest, the questions remains: if they can screw over the people in their life they are supposed to hold most dear, what's to stop them from screwing you?
Politicians are free to have private lives and do more or less what they wish when they get home with whomever. But when the public is availed of knowledge of the core dishonesty of one its supposed servants via adultery, all of the promises and intentions of that individual may be called into question.