As a Jeffersonian Constitutionalist and a member of a sizable subset (albeit still a minority) of voters, I am very interested in this topic.
I fully agree with the idea that our government, state and national both, should be held to high ethical standards and conduct themselves with politeness and observe all good manners. However, I see no need to bring religion into the discussion of government. Socrates, Aristotle and Aesop - among many others - were promoting and discussing ethics and morality long before any church or religion became involved.
I found some quotes from my main politician, TJ, helpful :
But it does me no injury for my neighbor to say there are twenty gods or no God. It neither picks my pocket nor breaks my leg. -Thomas Jefferson, Notes on Virginia, 1782
I inquire after no man's religion, and trouble none with mine; nor is it given us in this life to know whether yours or mine, our friends' or our foes', is exactly the right. - Thomas Jefferson, letter to Miles King, 1814
And, reluctantly, some books on how damaging religion can be in our politics :
Liars for Jesus
Over the Cliff