There are a number of arguments to be made about the positives and negatives of America's two-party system. This essay, though, is meant to address a few reasons why its unlikely that more than two parties in this country will ever have substantial political power without wide-ranging changes in our methods of elections.
In any election beyond the local school board or city council (in a few areas of the country), the single candidate with the most votes takes it all in what has been called a "first to the post" system. A candidate needs to get one vote more than the next best candidate to win it all. (This applies even in states like Louisiana where an open primary is held and the top two vote getters advance to a general election run-off, regardless of party affiliation) That means the person who garners the most votes is the sole representative of that ward, district, or state. With two parties, that's one vote more than 50% of the total, or 50% + 1. However, since in our system a plurality is all that is needed, it could mean that with 3 candidates, it could conceivably end up 34%, 33%, 33%. While almost 50% of the electorate in the first example doesn't get its choice, 66% in the second example are disappointed. Without awarding the political parties seats proportional to the votes cast in their favor, its unlikely that this system would support a viable third party.
In the sort of parliamentary system that supports having more than two parties, representation is awarded to the party according to how many voted on their line. We don't have that same proportional allotment. As our election system is now constructed, a multi-party election wouldn't necessarily lead to more a representational government but, in fact, could be less representative of the greater will of the voting public. Imagine a four-way race, each group having a special interest platform. Instead of 1/2 the voters getting at least a semblance of what they voted for, a 26% voter tally could mean that a party with a very narrow focus, even what might be a fringe position, could end up 'representing' the other 74% who have little or nothing in common with them. This is the sort of outcome that is possible beyond a two-party race in a winner-take-all system. Unless America moves to design a method of electing legislative representatives proportionally, who would then form coalitions to pick our federal officials, a two-party system is the most likely scenario we will have.