The founders of the United States of America were not trying to create a Christian nation in 1776. But they did view the Christian faith as beneficial to the type of republic they hoped to form. The man who led the way in articulating this benefit was John Witherspoon, a Presbyterian minister and influential founder who flies under the radar of most American history classes.
Witherspoon contended that the contribution of "true religion" to the public order is the morality of its people. If we were to translate this into our contemporary lingo we'd say, "The gospel's influence on society is transformed lives."
Witherspoon's explanation is a piece of very applicable logic.
[Read the rest of the article at Desiring God.]