If both sides -- those who want a third party and those who want to change the Democratic Party -- were well organized, they could forge an alliance: divide up districts between them, pledge to support third party candidates where that's the best choice, and pledge to support left-wing Democrats where that's the best choice. But the thing is that neither side is well organized nationwide, so it's impossible to create such an electoral pact at this point.
[WS:] Good point, Yoshie. The problem is, however, that it is rather difficult to be "well organized" for groups that have different agendas, interests and goals. It is much easier to "organize" people preoccupied with single issues. Since the right tends to be more preoccupied with single issue agendas (crime, security, morality, etc.) than the left - being "well organized" is inherently much easier for the Republicans than for the Democrats.
I think that much of the Left talk about being organized is akin to the much of the Right talk about being personally responsible. Both tend to focus on the individual and his/her devotion to a set of values (either liberal or conservative) while underplaying systemic factors. Telling the Left which by its nature encompasses diverse interests, goals, and agendas to "get united and better organized" is akin to telling someone who grew up in a ghetto and did not even have a chance to acquire marketable skills to "be more responsible and work harder."
In short, the call for "being organized" is a call for a single agenda where there is a multitude and variety. In the US context - with the majoritarian electoral system - it is very difficult to accomplish. Perhaps the only viable form of unity under such conditions is "hold your nose and vote for the lesser evil" - to which Democrats are well adapted. Any other form of "organization" or unity on the left is pretty much outside the realm of possibilities under the current electoral system.
To my knowledge, the only workable institutional system that facilitates unity amidst diversity is the European-style parliamentary system based on the principles of corporatism and proportional representation. I also think that this is by far a more attainable goal in the US than, say, "getting rid of capitalism," or "starting a revolution."
Wojtek