I've never understood how these so-called strict constructionists can so blithely toss out parts of the constitution that they disagree with. If the framers had desired to merely prohibit congress from creating a federal church, then they would have written that. Instead, after consideration and debate, they wrote that congress should
make no law respecting the establishment of religion.
Many people, including such prominent leaders as Patrick Henry, argued strongly for some form of government support of religion, feeling that failure to acknowledge God, or Christianity in particular, in the new nation's founding document would doom its chances of success. Others, including Thomas Jefferson and James Madison, disagreed. Looking back on the destruction religious wars had caused since the Protestant Reformation, they believed that the surest way to achieve the domestic peace necessary for free and orderly economic activity and to avoid the oppression and injustice caused by various forms of religious establishment, was to separate the religious and civil realms.
There's more here:
http://www.opposingviews.com/arguments/jefferson-madison-and-the-separation-of-church-and-stateWhen Jefferson's bill came up again in 1786, it passed by a vote of 60 to 27. In an attempt to give some kind of official recognition to Christianity, some assemblymen tried to insert an acknowledgment of “Jesus Christ, the holy author of our religion.” Jefferson took pleasure in the fact that “the insertion was rejected by a great majority, in proof that they meant to comprehend, within the mantle of its protection, the Jew and the Gentile, the Christian and the Mahometan, the Hindoo, the infidel of every denomination.”