Answer and Explanation:
The Constitution itself establishes a representative democracy, or republic, not a pure democracy. In that sense, I guess you could say it's "undemocratic," although that word seems to have connotations about the electoral process that aren't exactly accurate.
The framers of the Constitution were very concerned about a majority rule changing fundamental laws. While they made the Constitution a flexible document that provided for the possibility of amending, it is an extremely laborious task to do so. The idea is that no temporary majority can significantly affect the rights and protections of the citizenry.
To a large extent, that changed with one critical writing. In 1905, Justice Oliver Wendell Holmes, Jr. wrote the dissent in Lochner v. New York which established the concept of an "empty Constitution." That means that the prevailing legal theory to this day is that the Constitution does not in fact establish *anything* and in lieu of judicial precedent, the will of the people at any snapshot in time is effectively law. This is typically a leftist judicial outlook.
One of the biggest ironies of this decision is making it's way through the appellate courts right now: the California Prop 8 issue. Of course the leftists (rightfully) side with those who support gay marriage. However, if the case is to be decided in their favor, i.e. that a majority cannot vote away someone's right, it will be a repudiation of Holmesian doctrine. If the courts uphold the Holmesian standard, they will be forced to rule that the popular vote can, in fact, restrict rights of the people--in this case, the first amendment right of freedom of association.
