how long do potatoes last?

I have a bag of potatoes on the patio.  Cut the hulmes off 2 weeks ago and was planning on eatting them in the next few days.  However, the bag of spuds that I was hoping to grow for Christmas is doing absolutely nothing.  Can I keep the cut ones, still in compost and not messed about in any way yet, in the bag until the big day or will they rot?  I know it sounds crazy but only 4 of us there and really want to treat the famly to homegrown food and not have to come to fisticuffs over the last bag of spuds in the local shops!!!