An explanation is required. Both Governor Sanford and Senator Ensign are more or less fundamentalist Christians. Even more, they are heavily influenced by 'The Family,' a strain of Christian fundamentalism that apparently weds the language and appearance of the gospel to a version of the explicitly anti-Christian philosophy known as Objectivism. They are a sect which has determined that to feed the hungry, to care for the sick, and to visit those in prison is a waste of time, and the group that really needs our love and service and compassion are the rich and the powerful, who are, according to this creed, the foundation of our society, the virtuous ones who innovate and produce jobs for everyone else, etc. It's sort of a 'prosperity gospel meets Ayn Rand and makes sweet sweet love while crushing organized labour beneath its boot heel.' When they speak of serving the poor, or having a heart for the poor, they mean serving powerful businessmen and having a heart for powerful members of congress: the 'poor in spirit.' The poverty of the spirits of businessmen and members of congress may even be well established, but that's hardly what Jesus was talking about, and is, of course, neither here nor there.
As dictated by their fundamentalist faith, these men do not believe that they were put into power by their constituents. No, it was God who appointed them to their current posts. They are His elect, you see. His chosen. It was His hand which guided the election, explicitly not the votes of everyday people. They are therefore, in their own minds, not answerable to the people, but only to God. To resign now would be to act against the will of God that they use the positions to which they were divinely mandated to receive for the advance of the cause of His kingdom on Earth, and is therefore impossible.
That's pretty much all there is to it. Theocracy or bust, and no amount of naysaying will convince them of anything else. Come face to face with their own moral bankruptcy? Well, God's only testing them. Testing their resolve, and their willingness to submit to his will and to remain in the office to which He appointed them. And besides, God doesn't care about whether or not they've shown themselves to be hypocrites, or whether or not they're virtuous men. God just cares that they're obedient men, doing the work for which they have been Chosen. And by their own reckoning, they are.
It's disgusting, yes. Hypocritical, yes. Unexpected? Hardly.