It's really important that we all be clearly informed abut the Constitution on this matter. I understand that there's best selling book out there from a right wing perspective arguing just the opposite. For the life of me, I don't see how they do it -- but they do.
It was the national Congress, but "not with my approbation [approval]," said James Madison (Hunt, Writings, 9:100), which unconstitutionally hired the first congressional chaplain. It was during the Civil War when the words "In God We Trust" first appeared on some national currency, but it was not until 1956, by an act of Congress, when those words first appeared on all U.S. currency. It was in 1954 when Congress put the words "under God" into the national pledge of allegiance, which pledge no longer represents all American citizens. Therefore, the monumental lesson to be learned: religion liberty is in most danger when the national Congress and state legislatures are in session. "Strongly guarded as is the separation between Religion and Government in the Constitution of the United States, the danger of encroachment by ecclesiastical bodies may be illustrated by precedents already furnished in their short history," James Madison, (William and Mary Quarterly, 3:555).
If you haven't explored this much, you might like to take a look at the webstie of Americans United for Separation of Church and State.
Gene Garman, by the way, is a religion major graduate from Baylor University, Waco, Texas and has a Master of Divinity degree from Midwestern Baptist Theological Seminary. Traditionally in this country, Baptists have been VERY strong supporters of separation of church and state. Sadly, the support has dwindled hugely over the last few years. Many people don't realize that those of us against tearing down that wall are as concerned about the potential for the government's interferece with religion as we are religious interference with government.