Can I reduce my offer?

I made a cash offer on a home that needs a lot of work. It was accepted and signed off on, "as is." There was only one expensive surprise when I had an inspection, which was that the HVAC system is ancient and possibly doesn't work (the homeowner said it did, but was using a space heater during our viewing). I agreed to give until the end of January to close, but about a days before closing, it was discovered that the homeowner hadn't prorated her husband's will, and we don't know how long it's going to take. A lot of work needs to be done before we can move in and now I'm really concerned about rising construction prices. Do you think I have a basis to reduce the offer?