At the far left of the political left are what are referred to as "progressives." Progressive politics centers on reform of and change from traditional and conservative (historical models), and emphasizes a change to the old and worn out ideologies, including the traditional ideological stances of both conservatism and liberalism, and based upon the concept that the world is dynamic and needs dynamic changes in the political sphere to meet them.
I would be one of those. In fact, there is an entire slice of political independents that are known as Independent Progressives, and that is where my politics are. Unfortunately for us progressives, however, the Democrats have a tendency to want to keep the power structures of the government about where they are, and perpetuate their own place within them. The progressives' choice for a presidential candidate in 2004 was Howard Dean, and they reluctantly backed Kerry once Dean fell out of the race. Progressives were divided unequally between Edwards and Obama early in the 2008 primaries, but Obama appealed far more to moderate independents and so he gathered more steam than Edwards early on because he had a broader base of support. Generally speaking, progressives did not show much support for Clinton due to the centrist triangulation policies of Bill Clinton during his administration.