Be cool. You're not in any danger. Stay calm and don't escalate. It's not unusual for a first teaching job in China to not work out. You'll get your passport and be on your way pretty quick.
I would be really surprised if the PSB did anything to get involved other than just telling each side to work it out, but if the school did give them your passport, I'm sure they'd give it to you straight away. Whatever happens, the passport is yours/US govt property. You don't need to agree to anything or sign anything to get it back into your possession, but you can know this confidently without having to say it loudly. Everyone else knows it, so if you sit still, it will pretty much come your way.
Maybe there's something you can do to make a graceful exit that will be good for all, and I wouldn't be too hasty about leaving China. Why not look for another job? It takes a while to get used to the place, so don't worry about a difficult time on your first go and there's no need to necessarily run off to Beijing. You might find another job in the same city or Harbin, or wherever.
For someone coming to and teaching in China for the very first time, I don't think it's at all surprising to have some problems like this. The school should understand your adjustment period even if they don't want to admit it, but you can probably also understand the school's interest in this. Their demanding money is just like someone already said, it's saving face and also a bargaining position to have an advantage in case anyone wants to take sides or lay blame.