In my experience, the other guy has it right: "Small-d democrat" means someone who supports democracy (... enough compared to some base line in whatever context

In my experience, the other guy has it right: "Small-d democrat" means someone who supports democracy (... enough compared to some base line in whatever context that it's worth discussing), not someone who weakly endorses the Democratic party. A small-d democrat may be an avid big-D Democrat, or a weak one, or not one at all. I'm sure a big portion of the Republican party are small-d democrats when the alternative is monarchism.