Shaky assumption
You're making the partisan assumption that Democrats agree with Bush that supply-side stimulus will work, but simply don't want stimulus for political reasons.
A more reasonable assumption is that they genuinely disagree on the value of stimulating the supply side when all the economic numbers say that the demand side is depressed. Their alternative plan is a concrete expression of their position because it's targeted at the demand side. It weights the tax breaks toward the middle class, who, being generally strapped for cash these days, are likely to immediately inject it into the economy by making a lot of smaller purchases of staple and general consumer goods. They'll spread the stimulus over a much wider population.
--Robert