the intention of the framers and what we are now are not one in the same. yes, we have elected officials who represent us but we also have ballot referendums which are clearly not what the framers such as madison had in mind when setting up our "republic". also, the two forms of government are not mutually exclusive. we have a republic that is very disimilar to the roman republic (theoretically at least) in that we were constructed in a fashion that was meant to avoid the election of nobles only and an oligarchy as a result. in that sense, we are really more or a representative democracy. references to town hall meetings and tea parties are direct references to a democracy and not a republic. the creation of the cons ution itself may have been a reaction against democracy, but the dominant trend over the last two centuries has been to make our government into a representative democracy.
so even if the framers were not about democracy, the people already were. the demands of the people to vote were taken into consideration by the framers and this is why they wrote several anti-democratic provisions into the cons ution. the senate was not to be elected directly by the people; the president was not to be directly elected by the voters, and the supreme court was to be appointed. and more importantly to the "is this a democracy-versus-republic debate", the cons ution left the question of who could vote in elections to each individual state. so the first federal government that met in 1789 was a republic with only an iota of democratic representation. this is what people mean today when they say America is a republic, not a democracy (when not parroting the cliche du jour that is). the fact is that the passage of the 17th ammendment essentially made us a representative democracy.
as to your latter point, your antecedent leaves me at an impasse. is the "government of which [i] speak" the quasi-democracy you have implied the rest of the united states is not, or is it the corporate based oligarchy that we have since become under the banner of neoliberal policies ?