The United States was not founded as a "direct democracy." On the contrary, Article I of the U.S. Constitution, which establishes a bicameral legislature, was intended to eliminate the notion that the emerging nation would or could be a direct democracy. The establishment of a House of Representatives and of a Senate established the foundation for what is called a "representatives democracy," or a republic. Among the most influential authors of the draft constitution that would emerge as one of the most important documents in human history, James Madison was a forceful advocate of democracy. He was equally concerned, however, that the form of government that replaced fealty to the British Crown not be undermined by factionalism that he felt would inevitably emerge in a direct or popular democracy in which each citizen -- at least among adults -- would vote on every issue that came before it. As Madison wrote in Federalist Paper #10 regarding the impracticality of popular government versus representative government,
"The instability, injustice, and confusion introduced into the public councils, have, in truth, been the mortal diseases under which popular governments have everywhere perished; as they continue to be the favorite and fruitful topics from which the adversaries to liberty derive their most specious declamations. The valuable improvements made by the American constitutions on the popular models, both ancient and modern, cannot certainly be too much admired. . ."
The Constitution established a legislature designed to provide for representative government that would be guided by certain specified principles and guidelines intended to preclude the factionalism that the Framers agreed would be too precarious and divisive to survive the trials that lied ahead. The alternative to direct democracy, one that would preserve the concept of liberty, involved the establishment of the republic that survives to this day. To again quote Madison from Federalist #10:
"A republic, by which I mean a government in which the scheme of representation takes place, opens a different prospect, and promises the cure for which we are seeking."
While many scholars, politicians, and pundits have repeatedly emphasized the "citizen-legislature" model that they believe precluded the emergence of career politicians who serve for decades and for which limits on the number of terms an individual can serve in Congress remains an attractive proposal, Madison and others were equally wary of the threat to the Union that could accompany the institutionalization of amateurism. There are no term limits on legislatures in the Constitution not because nobody thought of it, but because representative democracy demanded the kind of knowledge and experience that would provide for the true representation of disparate communities without allowing for fissures that could threaten the stability of the Union.
In the United States, we have an indirect democracy. Direct democracy would be completely unworkable in a country the size of the United States.
In a direct democracy, all citizens deliberate about and vote on all proposed laws. This is why it is called "direct." The citizens rule for themselves rather than electing representatives to take their places. This would be very difficult in a large polity because not everyone's voice could be heard in debates in any sort of a timely manner. In the US, we do elect representatives and they make the laws for us. Therefore, we are not a direct democracy but, rather, an indirect democracy.