For your situation, I'd say 1 month max... If you're hanging around too long, even the people you think that you can trust will ditch you, plus lots of employers do have the mentality of "if I get rid of this person, there's 3 lining up to take his position" or even "why the hell is this guy still leeching around if he got something else lined up?"... But of course, if they let go of you before the transition, then you'd either have to find another job to survive in the meantime, or survive off of your savings or what little amounts the state will give you until you transition there, and even then sometimes it's not a done deal... The other company could also easily hire someone else as well and you'd be in an interesting pickle, which I have experienced before but luckily I found a lower-paying, but immediate hire job in the area, otherwise I would have moved to that area for naught.
So in reality, sentiments aside, it's water off a duck's back unless you're, for the sake of example, as valuable as Kim Peek (below). But average job is about 2 weeks, or the day of with a bridge-burning nasty letter if you really hated that job
