To understand the founders of American democracy, and the system of government they devised, it is not enough to stand in the present and look back at 1787. You have to stand where the founders stood, and then look back, from there, at the past they knew.
In trying to create a constitutional government, they had few models. One was the British constitutional monarchy, before it was corrupted (as they saw it) by George III. Everywhere else in their world, with a few exceptions that seemed not to suit the American model (Switzerland, Holland) absolute monarchs ruled from their palaces by God's decree, answerable to no one.
But the founders had a rich resource of government models in the histories of the Roman republic and the Greek city states of antiquity. These were not obscure subjects: the founders were steeped in classical learning through their shared education. They had all grown up in the same method of schooling that had predominated in the Western world since the Middle Ages, a long litany of Greek and Roman authors, read in their original languages.
They thought through problems, both personal and political, in classical terms. The classical authors provided the founders with their symbolic language when they wrote to one another. There are hundreds of instances of classical analogies in the generation of the American Revolution, from the designs on the national seal to the name of the national Capitol. One of my favorites is Cincinnatus. He was a Roman hero who, during a crisis, reluctantly accepted the dictatorship for six months, defeated Rome's enemies in six weeks, then resigned and went back to his plow.
Now regarded as almost surely mythical, Cincinnatus was a real hero to the founders. And when George Washington resigned from public life in 1783 after the great victory and returned to Mount Vernon rather than mounting the throne of the new nation, he was the marvel of the world, and he was behaving quite deliberately on the classical model. His peers recognized it. Washington became head of an association of Revolutionary War veterans -- the equivalent of today's American Legion or VFW -- called the Society of the Cincinnati.
(Washington agonized later when an equally classical sense of civic duty led him to return to head the Constitutional Convention and later to accept the presidency.)
The idea that this country was founded on "Judeo-Christian principles" by "Bible-believing men" is a convenient fiction for the Pat Robertsons of the nation, but if you take that as your starting point, the real history of the founding will be utterly incomprehensible. A Bible-based vision would have hailed Washington as Moses, leading his people out of bondage. But there was none of that in 1783. No doubt the founders assumed that the institutions they were creating would be used by people who were more or less Christians (some, especially Madison and Jefferson, thought about this a good deal), but the models they studied before they built this system of government were not in the Bible (which, after all, never claims to be a manual of political theory), but in Tacitus and Xenophon.
Not the truth of the classical world, but the version of it that was understood by the Enlightenment, the version enshrined in that canon of (surviving) classical writing that the founders learned in their schoolboy days: the Greek and Roman historians, most of them "nostalgic aristocrats disgruntled by monarchial and democratic encroachments" on the power of their class [Richard]. Writers like Thucydides, an aristocrat exiled by a popular government, who wrote a horrific description of the irrational, unstable, violent government of Athens under the popular demagogue Cleon, who cost that state dearly during the Peloponnesian War (and, incidentally, led the party that exiled Thucydides).
The founders had these models in mind when they framed America's government. They also had in mind a theory of government inherited from the same antiquity. Plato, in the 4th century B.C.E., laid out three simple forms of government: monarchy (rule by one), aristocracy (rule by a few) and democracy (rule by the many), explained what was wrong with each, showed how each deteriorated over time, and suggested that the best form of government would be one that balanced these three orders of society. It came to be called the "mixed government" theory, and Aristotle enshrined it as the centerpiece of his Politics.
Other classical writers (Polybius, etc.) concurred that only mixed government could prevent cycles of violence, slides into tyranny or mob rule, decay of liberty and public virtue. After its fall, the old Roman republic was mourned (probably falsely) as the perfect example of mixed government, and the nostalgic fondness for it in Plutarch, Livy, and many other late Roman authors confirmed many of the Founders in their sense that this was the best path for America.
The Federalists built the notion of mixed government into the U.S. Constitution. In many details, they strove for a balance between the one president, the few senators and the Representatives of the many.
Not everyone who participated in the founding was convinced about mixed government, however. Those who thought the new country could bear a pure democracy based their hope on America's agrarian nature, though this hope, too, was rooted in the ethics of the Roman republic. To Jefferson and Madison, the secret of the ancient republics' successes was not their mixed form of government, but their pastoral values. "Cultivators of the earth are the most valuable citizens," Jefferson wrote. "They are the most vigorous, the most independent, the most virtuous, and they are tied to their country, and wedded to its interest and liberty by the most lasting bonds." His famous conclusion was that "our governments will remain virtuous for many centuries; as long as they are chiefly agricultural; and this will be as long as there shall be vacant lands in any part of America."
The modern American government is a hybrid of mixed government with representative democracy, brought about mainly by the rise, in the last decade of the 18th century, of political parties which cut across class lines, whose division replaced that which was intended among the branches of government. To those who had grown up believing in mixed governments, this was alarming.
Washington devoted most of his Farewell Address to an attack on this development. John Adams wrote in 1806: "I once thought our Constitution was quasi or mixed government, but they (Republicans) have now made it, to all intents and purposes, in virtue, in spirit, and in effect, a democracy. We are left without resources but in our prayers and tears, and have nothing that we can do or say, but the Lord have mercy on us."
It would get worse, for the mixed government purists. The selection of the Electoral College gradually shifted to the popular vote (by 1828 only South Carolina and Delaware still chose their electors through the state legislatures). This and the 17th Amendment, which provided for the direct election of senators, in 1913, were the greatest blows to the mixed government created in 1787. Yet aspects of it remain, in the appointments-for-life of Supreme Court justices, for instance, and in the Electoral College.