Frank Fleming's flamboyant rant on third (and fourth) political parties at Pajamas Media is both fun and instructive:
The problem with third parties is that they always take from the extreme ends, weakening just one of the parties and leaving the party with the opposite views of the third party the strongest. Just listen to liberals whine about Ralph Nader for his part in the 2000 election. Also, third parties attract all the crazies -- all the people who give up on the social niceties (read: "sanity") -- needed to be a member of one of the major parties. For instance, libertarians have seemingly rational stances of fiscal conservatism and social liberalism, but who does the Libertarian Party nominate? Candidates who dye themselves blue and like to have their promotional pictures taken with ferrets. The only real way a third party could be viable would be to steal the moderates out of both parties, which would basically be a repeat of Obama promising some ephemeral hope and change and no specifics (specifics and principled stances scare moderates).
Naturally, I have a certain sympathy for multi-party systems - as I've been thoroughly indoctrinated during my years abroad and daily eye the cool-aid with mounting thirst. However, the paramount problem with a third party in America is our presidential, rather than parliamentary, emphasis. Dividing a consequential, winner-takes-all, one-shot election is suicide. The Tea Party, for example, could command serious reform (on the right, at least) if they controlled a dozen votes in the House and a couple Senate seats. That's the foundation of coalition government, and it lobbies well for compromise from the establishment.
Everyone would know that Tea Partiers were simply schismatic Republicans - and that would be fine. If seen as a sensible, mainstream alternative, they'd give the GOP an interesting diversity, allow unrest to flow somewhere other than the Democratic party and give the right a bi-partisan, open-to-compromise-and-new-ideas gloss. But, unlike the Green and Libertarian parties, the Tea Party and GOP would need to be seen as embracing one another as worthy allies and adversaries.
Of course, the better idea would be for the GOP to usurp the Tea Parties main themes. But the GOP has been giving lip-service to those ideas for decades - and no one believes them any longer!