It has historically been one of the fundamental characteristics of the American political structure that unlike other Western countries you never got a Labour party. Why should it happen now, when trade unions are weaker than ever? Who should organize it?
(it seems like wishful thinking on your part..)
I am inclined to agree, and would add that most social democrats in the United States have already been co-opted into the progressive wing of the Democratic Party. Socialists, Greens, and Libertarians have poor prospects for gaining traction in the polls because their voters can be courted by one of the major parties (which is something they will attempt at the very least for strategic reasons) if any of those minor factions starts to cost them elections by splitting the vote.
My suspicion is that with a multiparty system the U.S. would see at least a third of Democrats switch over to left-wing groups, allowing those who remain to better court moderate Independents. Getting libertarians out of the Republican Party might also help that group, as well - enabling them to shed some of their less palatable economic stances and appeal to lower-income earners who often like conservative values but are spooked off by the free market and Tea Party types.
At this point the best chance the U.S. has for developing a Labour-like faction is in young people being skeptical of capitalism. It is possible that they will gradually form a powerful democratic socialist / social democratic bloc within the Democratic Party, though it may be temporary seeing as people who grow up in the States after Millennials could experience economic conditions that do not incline them to be quite so critical of the establishment as young adults are now.
@Angus:
I agree with most of your post, though one issue with two-party systems is how they become de-facto one-party systems in many voting districts over time. My residence falls within state legislative districts that are consistently voting 70-80% for Republicans. The fact that Democrats run is a symbolic gesture - never a serious challenge. The tables are turned in many other places, as I imagine you are well aware. Even when a race gets competitive, we end up electing a bloke by whom nearly half the population does not feel well-represented. Maybe a lot of folks are okay with it but I certainly feel disenfranchised in an informal and indirect, yet institutionalized, apparently socially-acceptable way.