Doesn't quite look like anything I've seen. It might be discarded skins from aphids, or maybe whitefly eggs, but doesn't look quite right for either one. Check under the leaves - if you see more white things, it's probably whitefly eggs. Check the new growth at the tips - if you see small, pear shaped bugs, they're aphids. Either way, I would get a horticultural oil or soap and spray the plant all over, getting the undersides of the leaves too, and segregate it from the rest of your plants until you get it under control.

Idea - try a strong shower first and see if the white stuff washes off, let dry, and THEN spray.

Thank you watergal, I will definately isolate it and clean it up, I'll try the shower first as well and then spray it. I took an old toothbrush and tried to scrub some of 'it' off of a small area, whatever the stuff is it's really hard to remove. There are no aphids and there aren't any white flies, so far... but if it's eggs then maybe they just haven't hatched yet. The leaves seem to be the only area unaffected so far. Fortunately it's warm enough where I am now that I can place it outside again, so if it's eggs on there, they won't hatch in my house!!
If all else fails, I'll give my baby up for adoption to someone with less fear of bugs in their house over the winter!
Thanks again for your help!