Even a cursory scan of History reveals a significant involvement presence of "God" in governing. And the records show that it wasn't a particularly "hard" sell; a vast majority of human beings all over the planet have an instinct to look to a "higher power", while any and all of those who wished to govern found it both effective and useful to claim direction from an unassailable higher being that could be challenged at the human level. Even today, we see religion playing a huge role around the world in establishing a "right to rule."
Countries and Rulers who attempted to eliminate any reliance on authority from a higher power have been seen to have a limited shelf life. The exist as long as military force supports the head of State, but collapses when that support disappears, usually accompanied by a lot of ill will.
A common view is that this is because of two elements: 1) as mentioned above, it is nice for a ruler to be able to play "good cop" to God as the "bad cop" when ruling...it allows the human to take credit and kudos for the good things, and blame the bad things on an unassailable and unreachable entity with unlimited power and authority; and 2) many people truly believe in an "Almighty God" and do not need significant convincing to accept the concept.
The Founding Fathers clearly saw that any successful governing entity required the granting of authority of a Higher Power, stipulating that the right to govern was given man by God, and was inalienable. They depended on the concept that by placing governing power in the hands of many, there would be less chance of any one individual claiming, acquiring and exercising his or her personal views by representing them as God's will. All of those who were influential recognized the challenge. Some were expecting success...probably the majority. Others, like Jefferson, thought that the attempt had promise but a limited life span; as he said, "ultimately government becomes the enemy of individual freedom." And they all recognized that the time could very well come when the government they founded would cease to be responsive to God and the People, thus requiring still another revolution.
When there is a general acceptance that governance is ultimately responsible to "God" there is a tendency to grumble when personal lives don't go very well...but most of the time (with exceptions, like the French Revolution) that is where it stops. For more to occur, the "stand-ins" for God have to be supremely stupid...and that does occur. When there is no concept of authority from God, it is much easier for those who object to governmental decisions to brand them as unacceptable and to claim just as much right to rule as does the person in charge. Thus...governmental chaos can occur, followed by a period of optimism to be followed once again by chaos...and so forth.
America has evolved into a state of confusion in this regard. We still have "In God we Trust" on our money. A majority, as slim as it might be today, still sees us as a Judaeo-Christian country that looks to the moral elements of the ten commandments as imperatives. At the same time, our Supreme Court has seen the Constitution's ban on "establishing" an official religion, a ban designed to allow each person the right to worship God in his or her own way, as a direction to remove God from public places.
Similarly, the public and the courts have eroded the once automatic alignment of law and morals as delineated in the Ten Commandments, making legal all manner of activities that were once seen as unacceptable. Increased right to litigation has led to a remarkable lowering of standards considered previously as required civil behavior, the elimination of which once would have effectively brought about the shunning of the miscreant by all in a community. Now they appear to be on the verge of being the majority. Our leaders seem to delight in talking about God but ignoring God when governing.
Government, and human beings, make poor governors; both best succeed when they see themselves as tools, rather than the ultimate authority. At the very least, an elected leader needs to always remember that he serves all of the people...NOT as a God or an authority, but as a representative and servant. Politicians in our Republic have been quick to announce that they are elected because of their judgement and knowledge and ability to deal with many factors; they point to their background and relevant experiences as why they will decide for the people what the best decisions should be. I find this presumptuous and repugnant; I fail to understand why so many citizens just accept this balderdash as authoritative.
But no longer do our leaders look to the people for guidance as to what the people want. And they eliminate any concept of praying for guidance from any higher power either. They have determined to be an authority of and for themselves. The attempt to create a government for the people, by the people and of the people (with a presumption that all were accountable to "God") has become a government for the government and the office holders, by the government and the office holders, and of the government and its office holders.
It is hard to see how this will ever turn out well for what once was the United States of America.