The Democratic Party is, as I have said, a center-right political party. It is pro-capitalist, pro-business, and generally in favor of small government and low taxes. Democrats do not call for organizing workers into a revolutionary party to overthrow capitalism and institute a worker-run cooperative economy.
Marxism is a political theory that attempted to define a series of scientific steps to achieve a communist utopia. Marxist theory states that capitalism is a necessary phase in human social development, but that its inherent internal conflicts, which are caused by the struggle between business owners and workers, will lead to its downfall. Without getting into too many details, the idea behind Marxist theory, also known as scientific socialism, is that the exploited workers will organize into a revolutionary political party and overthrow the corporate system. Through a series of steps, the workers will consolidate power and work to create an egalitarian system where production is based on human need rather than profit. The end result of these steps is the dissolution of government itself, the "withering of the state," and the creation of a totally egalitarian society based on the credo, "from each according to his ability; to each according to his need."
If anyone can quote me a passage in the Democratic Party platform that even remotely resembles the above paragraph, I will be very surprised.
I just wish people would be slightly more careful when throwing around terms. Marxism is a very specific political theory. Neither of the two major political parties subscribe to it.