Making an important decision like this under pressure of time is sure to result in a mistake. You need to understand why Andrew has put you against such an immediate deadline. Is it because he has another offer for his services? Is it something you said or did? Is there anyone on the software team that would be able to give you the whole story? You need to see this as well as possible from his eyes, forgiving his words as rash judgement if possible.

My guess is that Andrew sees something that you don't...maybe that the software, after a certain amount is complete, can be finished by others and his services won't be needed. On the other hand, did Andrew do this at a previous company? Do you know? I would think you need to find someone that can take over Andrew's place if you decided you wanted to go on without him? Do you have this person? Anyway, I would not fire Andrew. I would use the time he stays on to find a replacement and figure out how to replace him. Also try to document what he is doing. This kind of blackmail works once in the corporate world. If it gets out that he has done this in the past it will make him radioactive with others.

I think the first decision is to buy time. Any ideas?