What other belief system could be the foundation for attempting to create a nation whose governance is based first and foremost upon the inherent, and Divinely ordained, freedom of all people? Some people like to respond in the negative by opining, "What, so only Christians are truly godly people?" That, of course is a loaded question. If we look to the modern day version of so-called "Christianity", we find watered-down, lukewarm, feel-good, politically-correct and sometimes heretical doctrines infiltrating the modern "Church", for the most part.
However, we are discussing the founding fathers' and Lincoln's belief-sets and how they were opposed to the occult and "New Age" doctrines promoted by the "seed of the Nachash (Serpent)". {No, I do not believe the "Serpent" was a snake, nor do I believe that Cain was the result of sex with someone other than Adam.}
However good intentioned and true-believing the founding fathers were, the reliance upon man to create and maintain a nation or government in full obedience to God's Will is impossible while we exist in this fallen state. We must understand that until the Kingdom of Heaven becomes FULLY manifest (it is here now in part as evidenced by Jesus the Christ's victory over the world, yet NOT fully realized) we are subject to our sinful nature and that of others. This is in no way a "doom and gloom" outlook; it is just an acknowledgement that we require the saving grace of our Creator by and through our Lord and Savior Jesus the Christ and I believe that Lincoln and the founding fathers, for the most part, understood that. However, as believers, we continue to strive toward following in Jesus' footsteps - true believers desire to act daily upon their faith.
Those who oppose that belief are of the Serpent seed; those who choose to rebel against the Creator and live in darkness while trying to take as many with them as possible. The subtleties of the lies which oppose Christ are as cunning as ever. Soullessness and/or paganistic "oneism" are the doctrines of choice for those who follow the adversary.
Without a strong faith, reliance and trust in The Father and our Lord and Savior, we may get "bluffed" by the original "poker-faced" Liar and his loyal minions. Always be on guard, for the adversary is lurking about even perhaps in places where you may feel safe.