This is a good question that gets into fascinating territory. I've written before to a small extent about the political thinking of the early American republic. Stanley Elkins and Eric McKitrick, in their early republic-spanning tome The Age of Federalism claim that democracy didn't "emerge as a fully legitimate cultural value in America...until the 1830s." What the constitution ushered into political being in 1789 was a republic that had some democratic features, but a republic is a different thing.
First we should establish what we mean by "democracy," because our modern notion of democracy is quite far from what early American politicians would have meant. Democracy meant, in a certain manner of thinking, chaos. Gordon Wood describes a particular crisis on the minds of the framers regarding "middling men" who, once appointed to a position in the militia, or taking a role as a government official, immediately assumed the bearing and manner of a "gentleman aristocrat." If all men could be so easily empowered and elevated, then government itself would be subjected to the tyranny of the masses, where demagogues and men high on rhetoric but low on honor could bottleneck the government. It fell, then, to men of "interest," men of proven worth and value, to steer the government in the right direction through the careful structure and intentional power-balance of a republic.
The republic would, in theory, channel the popular forces of the people through elected representatives who would then be subjected to the moderating forces of the government's structure itself. Thus the three-branch government, thus the bicameral legislature, the hierarchical judicial branch, the subordinate executive. All of these structures are meant to push and pull against one another, to slowly shake out a compromise that, in theory, results in the best-case scenario for the greatest number of people. Or, failing that, a compromise that would at least limit an imbalancing effect of a bad policy, etc.
This belief, that democracy was itself chaotic and immoderate, can even be seen in the fact that the Federalist party often used the word democrat as a pejorative for their political rivals, the Democratic-Republicans, whose own rhetoric on empowering the individual was seen as a ploy to exapand their own voter base.
There are obviously a number of issues that we can't talk about without breaking the 20-year rule, and one of the things about this early formation of government that i think people tend to overlook is that, while it does seem very easy to co-opt, there were unwritten expectations placed on men in government by culture that were obvious, omnipresent, and, as it turned out, temporary. In essence, there are no safeguards against bad-faith actors because the cultural expectation was that, given the obvious and careful structuring of the government, it was even in a bad actor's best interest to use the system as designed.
There are knock-on effects from this belief, as well. For instance, an unstated and hard to scry power retained by the 2nd amendment is less about an armed populace and far more about a robust organization that parallels the political structure. It's hard to convince an unwilling populace to participate in a war they don't believe in, for instance, and though this might mean a government less capable of waging total war, it also meant a citizenry with a strong sense of communal responsibility and belief in the power of organization.
I don't know that I'd take Wood at face value in his description of the government being formed as a group of reactionaries desperate to keep power out of the hands of "middling men" but there is certainly some truth to the idea that "the masses" themselves were a particularly dangerous aspect of democracy. From the view of a man in the late 18th century, this might seem self-evident: the War for Independence itself was birthed in part as a natural conclusion of a decade or more of violent public protest, and when men were unable to vote in a ballot booth they voted by action in the streets; by rioting, destroying property, targeting individuals with insult and comic punishments (think tarring and feathering), and by collective public action (like boycotts of english goods). Given that this was an expected part of the political world, why even consider empowering a group so inherently rowdy, violent, and destructive?
Elkins and McKitrick give a fairly typical top-down argument that the pathway to an empowered mass electorate was the result of mass political parties, who made expanding the franchise a priority which would help empower the parties themselves. That view itself is somewhat dated and there is value in approaching this question from the ground up, again given the enthusiasm of political character even for those men who were not already allowed to vote. But the date they settle on is more or less the accepted one, when the emergence of the Democratic Party ushered in the Second Party System. While the fine-tuned structure of the republic remained, much of its purpose had been somewhat circumvented by the expanded franchise.
I'm happy to answer follow-ups, I know that this was a meandering answer.
Gordon S Wood, Empire of Liberty
Stanley Elkins and Eric McKitrick, The Age of Federalism
Lawrence Cress, Citizens in Arms