Is Public Morality Necessary for Democracy?

[Helicitor]

I think our system of government requires some level of public morality, which I'll describe as adhering to societal norms and expectations even when no one is looking or will know. I think one such system of values can be summed up in the teachings by Jesus, such as stated in the sermon on the mount and the beatitudes, culminating in His request to "do unto others as you would have others do unto you." Since the Constitution prevents (rightly so) the Congress from establishing a religion, how CAN we establish and enforce public standards of morality? Are they even necessary?