The way to build a third party in the US is to do what the Greens are currently doing in Canada, the UK, and Australia -- pick a single seat. Elect somebody. The next election, keep that seat and elect somebody new. Slowly expand until you have a balance of power (like the LibDems do in the UK) at which point you should usually be big enough to survive a bad election and you can start behaving like a top-two party. (The 'you don't have to be careful anymore once you have the BOP', due to various reasons, has generally not been true in Australia, but in purer FPTP nations like the US, Canada, and the UK is usually the case). You can go ahead and run prominent people for the Presidency, but the mistake third parties make is focusing on that. Initially, when you have nothing, the focus should be on House seats.
There isn't much stopping the US from a system with a great deal of parties besides tradition and really stupid third parties. When a smart third party with an attractive ideology comes along, it will succeed. (I may actually try and do an AH timeline about Greens in the US in the late '90s, when they were popular, becoming a more successful party by focusing on House seats.)
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