I saw your previous question, I'm glad you came back for another shot.

The long and short of it comes down to how small of a group is required for oligarchy. Certainly for the first 145 or so years of US history, only a minority of citizens had the legal right to vote. This started with white, male property owners. The last property requirements for voting were finally abolished shortly before the Civil War. Then, for another 55 years after that, women were still not given the franchise until the passage of the 19th amendment in 1920. Only at this point can we safely say that a majority of American citizens had the legal right to cast a vote at the ballot box - that is, all white people. Of course, African-Americans were only given actual access to the ballot box in the 60s with the Civil Rights Movement and the Voting Rights Act. But this is just the legal sense of the term; it's just who has the theoretical legal right to vote, not who actually votes.

Given that voter turnout for presidential elections generally hovers in the high 50% range, and that it is much, much lower for off-year Congressional, all state, and all locals elections, one could convincingly make the argument that only a small group of people are actually exercising any control over the government through the ballot box, regardless of whether or not those people who are not taking part have a right to do so or not.

All of this doesn't even touch on the question of class - whether the "rich and powerful" or "special interests" are able to use their influence to the detriment of the rest. I'm sure there are lots of arguments that can be made for and against that claim, and I'm just not qualified - or willing - to jump down that rabbit hole at the moment.