Third parties in the US need to take a different form and have a different mission than they do in most other countries.
In much of Europe, governments are formed through a coalition of parties who agree to form a coalition government. That only happens after a general election that decides the number of seats each party will have in parliament. In order to form a government, various parties must agree to come together in such a way that they, together, can have a majority of parliament.
In the two-party system, each party tends to be made up of coalitions. The Dems consist of a coalition of unions, greens, education lobbyists, socialists, university professors, certain ethnic groups, Wall Street (yes, they break toward the democrats), etc. The Repubs are a coalition of farmers, small to mid-size businessmen, social conservatives, pro-lifers, low-taxers, a sizable portion of blue collar people, traditionalists, the religious right, and what some call the country club crowd, etc.
The differing elements of these coalitions can change party affiliation over time. For example, the vote of the black American was once a reliable one for the Republican Party on up to the second half of the 20th Century. Wall Street was once a reliable Republican bastion, and the American South was once completely Democrat. The Repubs were once the isolationist, anti-war party. The Democrats were once the party of states’ rights.
Once the parties form their coalitions, they form their platforms and loosely run on those platforms. The winning party essentially governs, but with a powerful opposition from the other party acting as a check.
So in Europe coalitions are formed after the election, while in the US that happens before an election.
Having said that, the real power in third parties can be illustrated by the 2009 special election in New York’s 37th Congressional District. New York’s Conservative Party candidate nearly won the election, but this was an anomaly because normally the Conservative Party prefers to endorse existing candidates from another party. They will only run their own candidate if they do not like the existing alternatives.
The Conservative Party does what the Tea Party people should do nationally. That is, if there is a viable candidate from one of the two major parties, endorse that candidate and run that candidate on the ballot as the Conservative Party candidate. If neither party has an acceptable candidate, endorse another candidate from a third party, and if there is no acceptable candidate, run your own candidate.
That’s a powerful recipe, and in fact it looks to me that this is the exact model this movement will embrace.