The idea that God has "blessed" America is integral to Christian Nationalists' religious and political ideology. This concept of a blessing isn't about God generally blessing humanity, but is instead the assertion of a special relationship between God and America -- a relationship not unlike the one described in the Old Testament between God and Israel. Without this special relationship, much of Christian Nationalists' religious and political agenda would be difficult if not impossible to justify. For this reason, the belief deserves closer scrutiny and greater criticism.
Christian Nationalists did not invent this. Puritans saw themselves as a "new Israel," repeating the biblical story of Exodus by establishing a "City on the Hill" in a "new Canaan" where a purer form of Christianity could develop and which would serve as a moral and religious beacon for the rest of the world.
In John Winthrop's day America's mission was to Christianize the world with Puritan Christianity. In the 1800s the mission was secularized to include "civilizing" the world alongside "Christianizing" it. Today, America has the mission to "democratize" the world, spreading the values of democracy and capitalism. Words change and concepts shift, but the similarities are greater and more instructive than the differences.
Framing America as a City on the Hill or "bright hope of humanity" causes it to stop being just a nation and to become, in addition, a religion. American soldiers are thus portrayed as having entered Iraq not only to liberate its people from a dictator, but also from darkness. American soldiers become missionaries for the True Faith -- the True American Faith. Instead of simply killing terrorists and insurgents, they also cast out demons. Americans themselves are not simply citizens of a nation or even of a great nation; instead, they are the "chosen people," blessed for living in the "chosen land" where a the divine project for humanity has reached its highest fulfillment.
"God Bless America" signs or banners are making both a political and religious statement about America having a special relationship with God that sets it apart -- morally, religiously, and politically -- from all other nations. Not only is this arrogant, but it serves to justify outrageous actions which wouldn't be tolerated if other nations did it.
This image is based upon a Nazi poster encouraging people to vote "Yes" in a 1938 referendum to legalize the Anschluss of Austria.