It only rarely works, and is due to a fundamental problem with the existing two parties not being able to adjust to changing voter opinion. The third party might end up either becoming one of the two dominant parties, or the major features of the 3rd party platform end up being subsumed by at least one of the prior two dominant parties. Either way, over time, third parties are blips.
You kinda contradicted yourself there, so I "fixed it for ya"in the true sense, not the smart-alecky sense.
This is a feature, not a bug. It leads to stability instead of the anarchy we see in, say, proportional representation schemes. Not only are PR schemes less stable, they have been shown to result in even less realized liberty than our two-party system.
To put it another way, the two-party system results in greater stability and more liberty as it marginalizes those at the extremes, even the liberty-minded extremes.
If the Tea party influences American parties in a smaller gov't/greater freedom fashion, they'll have done more good than being the usual misanthope-fest ineffective third party.