Third parties have a place in America, but rarely supplant an existing party. The real politics of it is that if a third party gains traction and gets above about 20% of the electorate's support, the major party who has lost members will choose to co-opt the third party's platform and, because of their experience and national positioning, will suck away the support for the third party.
The TEA Party is an example. They'll last a couple of election cycles, and if their members are successful, the Republican Party will totally morph to look like the TEA Party and the TEA Party itself will disappear.