Be patient, it will grow and sprout. You have done all the right things.

Yep. It will take a little time to get doing, but it will be fine.

Okay, so I guess I'm not patient. Had it on top of the water heater for warmth and checked it out this morning...and there is nothing there. It just looked like a cacoon that a butterfly had left. Oh well, I tried! I am curious, are these really rhizomes on Mandevilla or just fleshy, water-storing "bulbs"(for lack of better name)?. I see them on spider plant and asparagus fern also but have never seen new plants emerge from them either. I have brought my mandevilla up from the basement and put it in the south sunny window and watered it yesterday. It has small new green growth buds so wanted to get it going so by time it is ready to go out, it will have some healthy growth.

It seems that you found out that new plants will not grow from these tubers; they are, in fact, for water storage. See the reply to your posting in the Vines forum.

Here is a link that might be useful: Mandevilla tubers