1. America is a Christian nation.
Demographically, it is. According to an April 2009 Gallup poll, 77% of Americans identify as members of the Christian faith. Three quarters or more of Americans have always identified as Christian, or at least they have as far back as we can document.
But it's really a stretch to say that the United States has been run based on Christian principles. It violently broke off from the explicitly Christian-identified British empire largely over economic issues that included rum smuggling, slavery was part of the original package, and the only reason the land we now call the United States was available in the first place was because it was taken over, by force, by well-armed invaders.
If that's Christianity, what does apostasy look like?
2. The Founding Fathers would not have tolerated a secular government.
During the 18th century, there wasn't really any such thing as a Western secular democracy. The Founding Fathers had never seen one.
But that's what "Congress shall make no law respecting an establishment of religion" means; it reflects the Founding Fathers' efforts to distance themselves from European-style religious endorsement and create what was, at its time, the most secular government in the Western hemisphere.
The Founding Fathers were certainly not hostile to secularism. Thomas Paine, whose Common Sense pamphlet inspired the American Revolution, was a noted critic of religion in all forms. And to reassure Muslim allies, the Senate ratified a treaty in 1796 stating that their country was "in no way founded on the Christian religion."
3. Secular governments oppress religion.There's no evidence to support this claim.
Communist governments have historically tended to oppress religion, but this is because they are most often organized around cult ideologies that function as competing religions. In North Korea, for example, Kim Jong-il, who is believed to possess supernatural powers and to have been born under miraculous circumstances, is worshipped at hundreds of small indoctrination centers that function as churches. Mao in China, and Stalin in the former Soviet Union, were given similar messianic backstories.
But genuinely secular governments, such as those of France and Japan, tend to behave themselves.
4. The God of the Bible punishes non-Christian nations.
We know this isn't true, because no governments founded on the Christian faith actually exist in the Bible. The Revelation of St. John describes a Christian nation ruled by Jesus himself, but there is no suggestion that anybody else will ever be up to the task.
5. Without a Christian government, Christianity will lose clout in America.
The United States has a secular government, and over three-quarters of the population still identifies as Christian. Great Britain has an explicitly Christian government, but the 2008 British Social Attitudes Survey found that only half the population—50%—identifies as Christian. This would seem to suggest that government endorsement of religion doesn't determine what the population actually believes, and that stands to reason. Would you base your religious beliefs on U.S. government statutes?