Just about every time some one argues that the US is a christian nation they bring up the Pilgrims. Because the Pilgrims were christians of the puritan denomination that, according to legend, came to America for religious freedom, they somehow had something to do with the US Constitution about 160 years later. I think the proponents of a christian nation need to read more.
First of all, the Pilgrims were not the first North American colonists. It should be remembered that Native Americans with their own perfectly good religions were here for thousands of years before any of the usual suspects arrived. Then there were Norse, French traders, Spanish conquistadors, abandoned African slaves, and English colonists in Virginia, just to name a few, before the Pilgrims.
Second, they didn't come for religious freedom; they came for religious isolation. They had freedom to practice their religion in Holland, but what they really wanted was to get rid of the Church of England so they used the Dutch printing industry to print anti-C of E pamphlets which they smuggled into England. This naturally did not sit well with the head of the English Church, who also was King of England, James I. That made advocating the ouster of the head of the church sound remarkably like treason against the crown, because it was. Furthermore, they didn't much care for Holland with all those less pure christians running around practicing religious freedom too.
Third, when they got to America, they acted like a bunch of narrow-minded, intolerant jerks. The Native Americans in the region were helpful and tolerant, except when the Pilgrims stole food or desecrated their graves, and when the local tribes frequently saved the Pilgrims from starvation and death, the Pilgrims thanked their god rather than the people who actually did the work and provided the food. When any new English colonists arrived, they either had to follow the Puritan religion or they were banished, jailed, or, in at least on case, executed.
These are the great forefathers that advocates of a christian nation want to hold up as examples; people who would not have tolerated the religious beliefs of any of their modern admirers, who would have abhorred the kind of religious freedom advocated in the Constitution, and who were the kind of bores you would never invite to a party.