Marx's idea was the "dictatorship of the proletariat" and its evolution into a "classless society", without discussing the details of the governance, though he did quote the example of the Paris Commune (the following quote is from Wikipedia):
The Commune was formed of the municipal councilors, chosen by universal suffrage in the various wards of the town, responsible, and revocable at short terms. The majority of its members were naturally workers, or acknowledged representatives of the working class. The Commune was to be a working, not a parliamentary body, executive, and legislative at the same time. This form of popular government, featuring revocable election of councilors and maximal public participation in governance, resembles contemporary direct democracy.
I often hear people speak of democracy as the next, or the final, inevitable stage of human social development. Its inevitability is usually justified not by describing power relations that result in democracy being a stable attractor, but in terms of morality - democracy is more "enlightened". I don't see any inevitability to it - China and the Soviet Union manage(d) to maintain large, technologically-advanced nations for a long time without it - but suppose, for the sake of argument, that democracy is the inevitable next stage of human progress.
The May 18 2012 issue of Science has an article on p. 844, "Ancestral hierarchy and conflict", by Christopher Boehm, which, among other things, describes the changes over time of equality among male hominids. If we add its timeline to recent human history, then here is the history of democracy over time in the evolutionary line leading to humans:
There are two points to observe in this data:
I do believe "progress" is a meaningful term. But there isn't some cosmic niceness built into the universe that makes everything improve monotonically along every dimension at once.