Here is a useful historical study of the “Christian nation” question, The Founding Fathers and the Debate Over Religion in Revolutionary America: A History in Documents (OUP 2011), edited by Matthew L. Harris (Colorado State University-Pueblo) and Thomas S. Kidd (Baylor). The publisher’s description follows.
Whether America was founded as a Christian nation or as a secular republic is one of the most fiercely debated questions in American history. Historians Matthew Harris and Thomas Kidd offer an authoritative examination of the essential documents needed to understand this debate. The texts included in this volume – writings and speeches from both well-known and obscure early American thinkers – show that religion played a prominent yet fractious role in the era of the American Revolution.
In their personal beliefs, the Founders ranged from profound skeptics like Thomas Paine to traditional Christians like Patrick Henry. Nevertheless, most of the Founding Fathers rallied around certain crucial religious principles, including the idea that people were “created” equal, the belief that religious freedom required the disestablishment of state-backed denominations, the necessity of virtue in a republic, and the role of Providence in guiding the affairs of nations. Harris and Kidd show that through the struggles of war and the framing of the Constitution, Americans sought to reconcile their dedication to religious vitality with their commitment to religious freedom.