I used gum paste for the first time to make some angel figures for the top of a cake. I was expecting it to dry hard over night and they haven't. It's been 48 hours and it's still tacky. Any ideas of what happened or what I did wrong?
How big is the piece?
You must have made it thick. I use gumpaste all the time for my sculptures and some pieces take a months to dry properly, but I am sure they are all tons bigger then your piece. Put a fan on it and flip it. Do you live in high humidity? if so, make sure it isn't in a damp place to dry. I bet it is ready to go by tomorrow. 
Here is my latest sugar sculpture....... Sacred Heart III
Edited to add note after ready Peg818: Buy some silca gel packets to pack your pieces in so they keep you flowers and sculpted pieces dry.
I too am trying out gumpaste for the first time. It is scary to find out that gumpaste items can become soft after they have already dried out due to the humidity. peg818 thank you for sharing that info. 
I'm sorry that this happened to you, I'm sure you spent serious amounts of time only to have a mess. 
I hope you were able to save some of your flowers. dogheaven3 good luck with your angel.
Edited to add note after ready Peg818: Buy some silca gel packets to pack your pieces in so they keep you flowers and sculpted pieces dry.
The gel packets wouldn't have helped the flowers didn't totally melt but were soft the petals able to move just like a real flower, and they were on the cake at the show, it just was raining cats and dogs. The topper that i packed in a box by its self hardened back up just fine good as new.
Gum paste can take a very long time to harden, especially if it is humid or there is "cooking moisture" in the area. Here in Hawaii, I can have an almost hard piece and it will rain and the piece will be totally limp.
I have the closet size moisture remover but on some days even that doesn't help.
I leave it for a week, untouched.
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