All modern democracies are representative; it's for purely pragmatic reasons hard to see how a large community could govern itself directly by the people without introducing representative intermediaries.
The really interesting question for me is whether the United States, though formally a democratic republic, are factually ruled by a relatively small elite connected through family and business relations. It is surprising to a foreigner to see political family dynasties like the Kennedys or Bushes or Clintons (and now Trumps, for that matter). And one does not need to subscribe to conspiracy theories to recognize that the enormous wealth concentrated in the hands of a small number of billionaires results in an enormous political influence. The system of campaign financing through private donations appears to outsiders as a thinly veiled form of buying politicians, which obviously gives the enormously rich enormous political influence.
The questions to tackle here are:
- How large is the number of people "in power" through family or money?
- How well are the democratic and legal institutions protected against illegitimate influence?
- How well do the media work? How independent are they?
- The last two points determine the crucial question: Can the people form an opinion and express their interests in elections independently of and against the efforts of the elites in politics and media?
The current drift in the public political opinion is clearly showing defiance and independence of perceived elites, e.g. in Bernie Sanders' surprisingly strong campaign and in the rejection of Hillary Clinton in favor of the rogue candidate Donald Trump. This gives hope to the robustness of the democratic process.1
1 But even the public opinion swing towards defiance is developing under the ongoing influence of the elites. For example, Trump's rogue image may be mostly in style rather than substance, considering his wealth and politics benefiting the wealthy. The effect is that the economic elites have a malleable collaborator in power, but one who is perceived as their rogue opponent. This outcome may be pure serendipty, but it's hard to see how it could be any better.
The change in public discourse towards social media is ambivalent as well. Obviously a means to communicate directly with each other is prima facie a boost for a democratic discourse. On the other hand it clearly results in an abundance of false information, a loss in coherence in public opinion — which is not in itself a bad thing but tends to lead to echo chambers — and an increasing volatility in the public discourse: The news cycle is shorter, what is swept into the foreground is less predictable, and the ebb and flow of the discourse seems stronger than with traditional media.