i don't know anything about the US constitution... but if seperation of the church and state isn't in the constitution then it damn well should be. You only have to look at a lot of the non-secular islamic states to see the trouble a country can get into when church and state become too closely linked.
What the US Constitution says is that, "Congress shall make no law reguarding an establishment of religion or prohibiting the free excercise thereof." What that means is that the government cannot officially endorse a religion, require citizens to participate in a religion, or prohibit citizens from excercising their religion. I believe (I could be wrong about where it came from) that the phrase "separation of church and state" was taken from a letter written by Thomas Jefferson...and somehow people assumed that it was the Law of the Land.
I believe that the establishment clause is increasingly being misinterpreted to the point that its enforcement is violating the free excercise clause...I've read of several cases of this - prohibition of student-initiated, voluntary prayer in schools, the abolishment of religious (mainly Christian) clubs, and even one case where a school principle threatened to have arrested anyone who said "Jesus" or "God" at a graduation ceremony...whether in a speech or not.
Let every nation know, whether it wishes us well or ill, that we shall pay any price, bear any burden, meet any hardship, support any friend, oppose any foe, in order to assure the survival and the success of liberty.
~John F. Kennedy