Excuse me, the type of government our constitution established does NOT depend on anyone's definition of republican except that of the people who wrote it. They established a republic, not a democracy. You sound like Clinton and the definition of "is".
You've missed my point. While the Constitution establishes a Republic, most people read their own idea about what a republic is into that. What kind of a republic does the Constitution establish? Even among the Founders, there was quite a bit of debate about that very question. Generally speaking, the Constitution establishes a "liberal republic" (18th century definition of "liberal") such as was advocated by the colonial writer using the pseudonym Cato, as well as by Jefferson, etc. Thus, it IS an "indirect democracy", contra VWRCmember's claim above, because while containing republican elements of separation of powers and an implied emphasis on civic duty to be successful, our Constitution also very definitely established a liberal scheme for individual liberties, especially with the addition of the BoR, which necessarily implies a broad scheme of citizen participation, though through election and representation, rather than direct citizen control of policy and government (i.e. "direct" or "referendum" democracy). Democracy simply means "rule by the people", which is what we had with the Constitution, albeit in an indirect way.
The Constitution certainly did NOT set up a pure or "classical" republican (though again, I emphasise that there were elements of these in our founding system), which were more often oligarchies or aristocracies than anything else.