Steve, from my experience the major impediment is light. Even a crappy digital camera can take wonderful pics if you have enough light.
I've tinkered with the idea of getting a portrait light for this single purpose.
The lenses on the smaller crappy cams can actually be of great benefit. Since the lens is so small, the depth of field can be stretched, perceptually, to infinity. Really helps out with close-ups and macros.
Hmmm, portrait light or bubble king...