If you look back at the history of political realignments in this country, other than the formation of the Republican Party (which coincided with the industrial revolution and the push to develop the vast resources of the north american continent) they tend to happen within the two party structure. Advocating a third major party tends to miss the point - the political forest is made up of individual trees.
The Party affiliation of elected officials is very relevant in some ways and pretty irrelevant in others. It is relevant in terms of which caucus gets to set the agenda in the Legislature and Congress. It is not so relevant in terms of how legislation ends up actually getting written and what gets passed into law - not irrelevant, but not predictive.
Party affiliation is also less relevant to how campaigns and the vast majority of the business of politics and governance is conducted as well. Not irrelevant, but to take campaigns as an example, it is only one factor (and not the dominant factor) considered in how to win a competitive race. Who gets to be on Line A and Line B is usually pretty decisive - and there are those instances where for concrete reasons, that standard is superceded.
I respectfully suggest that the fact that realpolitik has triumphed (and Lieberman is a concrete and potent case in point) over the hankering - "left" and "right" - for some sort of ideologically pure fairy tale where the good guys are wearing white hats and the bad guys black hats is worth the time it takes to appreciate it. Acquired tastes often are.