I would be really interested for anyone to point out when, during any time in history, any "moral" government ever existed that obeyed every single one of God's commandments.
King David himself committed murder, adultery, and countless other sins during his reign as King over Israel. My point is not to bash King David, but to point out that a man described as being "after God's heart," who was appointed by God through the Prophet Samuel was capable of sin.
If you are looking for a "moral" government, you are looking on the wrong planet. The only place where a "moral" government exists, or has ever existed, is in heaven itself.
Christ said give unto Caesar what belongs to Caesar. Was this because Christ was advocating immoral governments? No, it was because we are not to build up our treasures on earth, but in heaven. Christ knew that no perfect government existed on earth, so why should we worry about returning the currency of the government to the government?
Americans in particular have this peculiar notion of creating this great Christian government so we can lead perfect Christian lives in our perfect Christian little bubble. Look at the Government under which the Apostles lived. It was a pagan empire and Christianity was a strange cult with a few hundred followers. Yet the Church flourished and God's will was done. If it could survive and thrive under those conditions, what does it say about our faith walk when we blame our government for not leading a moral life?
Pay your taxes, be a good civil servant, and follow God's commandments. The former is not in contradiction to the latter.