Political Wire digs up a particularly salient quote from Bill Clinton's My Life in which he makes essentially the same observation as Barack Obama, minus the word "bitter":
If [Republicans] could cut funding for Medicare, Medicaid, education, and the environment, middle-class Americans would see fewer benefits from their tax dollars, feel more resentful paying taxes, and become even more receptive to their appeals for tax cuts and their strategy of waging campaigns on divisive social and cultural issues like abortion, gay rights, and guns.
I do think Obama's words were poorly chosen, but I don't think they merit "Bittergate" as we're seeing it play out. Especially since this sort of sentiment isn't unknown to the Clintons, either.
--Kate Sheppard