Here's a snippet:
Rep. Earl Pomeroy (D-N.D.) who chaired the selection committee told the Times that while it did not officially rank the top three contenders for the post, House leadership was told that the majority of members considered Father O'Brien to be the most appropriate. Rev. Wright had actually come in third in the balloting, behind Rev. Dvorak.
The Washington Post reported that several Democrats "said they thought House leaders were trying to placate the religious right or were uncomfortable with naming a Catholic priest."
In an unusual move, O'Brien told reporters that he believed that had he been "of any mainline Protestant denomination," he would have been appointed to the post.
"I hope and pray that the 1960 presidential election did do away with the idea of Catholics as not being fully Americans," said O'Brien. "I'm not convinced that the prejudicial view is gone, and I do believe that if I were not a Catholic priest I would be the House chaplain."http://www.atheists.org/flash.line/congres4.htmCongress didn't always have prayer. A few of the first delegates argued for it, but it was soundly rejected. I'll have to research the cite for that, but I'm confident that it's true.
Edited to add (although there are other instances):
The United States was founded on the Constitution, not the Declaration of Independence. The Declaration of Independence was equivalent to an act of Congress and does not have the authority granted to the Constitution, which is the supreme law of the land. The Constitution does not contain the word "God." This was not an oversight. In fact, the original Constitution only contained one reference to religion of any kind: a statement that no religious test would ever be required as a qualification for public office. Moreover, there was very little controversy about this among the Founding Fathers.
When Benjamin Franklin proposed that the Constitutional Convention open with a daily prayer, he was rebuffed. And when the Founding Fathers decided to supplement the Constitution with the Bill of Rights, the very first clause of the First Amendment prohibited government establishment of religion.
http://www.infidels.org/library/modern/jeff_lowder/pledge.shtml