is common to hear people say that the United States was not meant to be a
democracy but a republic. But what does that mean? Perhaps nothing very
specific in many cases. But the Constitution tells us that the “United States
shall guarantee to every State in this Union a Republican Form of Government….”
(Article IV, Section 4) , and we would do
well to suppose that the Framers meant something specific by the term.
can’t look to the federal courts for clarification, since the U.S. Supreme
Court in 1849 “established the doctrine that questions arising under” that
section of the Constitution “are political, not judicial, in character and that
‘it rests with Congress to decide what government is the established one in a
State . . . as well as its republican character.’”  But similar
language “was contained in the Virginia Plan introduced in the [Constitutional]
Convention and was obviously attributable to [James] Madison.” 
So, what did James Madison mean by the term “republican”? In Federalist 14, he wrote that “in a democracy, the people meet and exercise the government in person; in a republic, they assemble and administer it by their representatives and agents. A democracy, consequently, will be confined to a small spot. A republic may be extended over a large region.”  And so, if we follow Madison in this, a republic is the sort of government we have in the United States today; and if all one means by saying he is a republican (small “r”) rather than a democrat (small “d”) in this Madisonian sense, then his philosophy of government is in keeping with the governmental configuration found in the federal and state governments. It is also true, that a democracy in the sense that Madison described it would be wholly impractical in all but localities with small populations.
But Charles Louis de Secondat, Baron de
Montesquieu was a political philosopher who was quite influential with the
founding generation. He said that “a republican government is” one “in which
the body or only a part of the people is possessed of the supreme power….” 
“WHEN the body of the people is possessed of the supreme power,” he said, “this
is called a democracy. When the supreme power is lodged in the hands of
a part of the people, it is then an aristocracy.” For him, democracy isn’t
a different kind of government than a republic, but a kind of republic; all
democracies are republics, but not all republics are democracies.
Now today, people call the United States a
“democracy,” or, perhaps more correctly, a “representative democracy.”
Montesquieu would agree with this terminology, since, regarding democracies, he
said, “They have occasion, as well as monarchs, and even more so, to be
directed by a council or senate. But, to have a proper confidence in these,
they should have the choosing of the members; whether the election be made by
themselves, as at Athens; or by some magistrate deputed for that purpose, as on
certain occasions was customary at Rome.”
Thus, in the United States, we have a republic if we use the terminology of Madison or Montesquieu. But the pertinent question, is whether we have, using Montesquieu’s terms, a democracy or an aristocracy.
At first, we undoubtedly had an aristocracy. Only white men with property could vote. And there were slaves to boot. Since that time, we have been moving in the direction of a democracy, and we now have, purportedly, universal suffrage. I say “purportedly,” because there have been continuing efforts to suppress the voting rights of black people down through the years up until today.
So, then, what do people mean when they say that we’re not a democracy but a republic? Some of them might just be talking nonsense, of course, but we should, without knowing otherwise, give them credit for cogency. If they mean anything coherent, they might well be arguing for a kind of aristocracy, where some people enjoy the franchise and others do not.