Oh my zeus, there is so much ignorance about America's history here it hurts. No, nowhere in the constitution does it mention the state as having to be secular, but ALSO nowhere in the constitution is "god" mentioned. In an age where religious phrases were everywhere, this can't have been anything but deliberate. (http://www.thenation.com/doc/20050221/allen)
Yes, the majority of people in this country are christian of one flavor or another, but the next largest group is people who don't subscribe to any religion. There are more people in the US who don't subscribe to a religion than there are Blacks and Asians COMBINED. (See CIA Factbook)It's fair to say that the US is a nation OF christians, but not A christian nation. This fact was illuminated in the Treaty of Tripoli, 1797. Article 11 states "the Government of the United States of America is not, in any sense, founded on the Christian religion" This treaty was passed unanimously (how many times does congress do that?) and many of the founding fathers were present to vote on it.
Furthermore, "Under god" was not added to the pledge until 1954, after a vigorous campaign by the Knights of Columbus, the nation's largest catholic fraternity. It was a successful attempt by the religious to extort the atmosphere of fear rampant in the McCarthy era and wed religion with patriotism. To be against the religion suddenly made you unpatriotic, which was a social death sentence in the 50's.
The "so help me god" part of the inauguration is actually not part of the offical oath. It was became popular after Roosevelt. Only 18 of the 43 presidents thus far have uttered the phrase at the end of their oath.
I think it's funny when people say it doesn't violate the establishment clause of the first amendment because "god" is not religion specific. It is. god = masculine, singular. This automatically excludes polytheists, female centered religions, and the non-theists. Everybody knows it means the judeo-christian god, hell, perhaps even the muslim god, but nobody wants to acknowledge it. It's evident by that little twinge of disgust you would get if they said "so help me Vishnu, or Sheba, or Zeus, or Jupiter, or Kinich Ahau, or Ra, or (insert never ending list of possible imaginary beings here).
I'm sorry if this pisses you off, but non-theists are never going to stop being treated as second class citizens by sitting down and shutting up.
PS. Oh, and not having "god" in the government would not be government professed atheism. It'd be neutral. If the money read "In god we do not trust", that too would be unconstitutional and would have to go. It's just best if the government didn't go there...