Since an oligarchy centers around a *few* elites running the country I vote No. . . but I see where people can believe it is this way.
Our country USE to be similar to an oligarchy but much less so, today, because of government expansion and an increased involvement in political activities by all citizens. Our Congress seats 435 members (Senate and Representatives) - on top of that there's the President, his cabinet and all others stationed to directly/indirectly influence political decision and knowledge. Per citizen involvement: White males who owned property were the only ones to be given the right to vote. Then it was all white males, then black males and other minorities and then women.
Political parties ran the newspapers and controlled what we "knew" - it's still a slight issue but not as much as before.
Also, more than ever, people's opinions have more sway over the acts and decisions of our politicians.
By all these changes and then some we've gone away from elitism and have become more of a balanced system which rests more and more in the hands of the people.