The city, of course, would be legally liable for any cost overrun. The reality in government is that if you have a three-way partnership of a third, a third, and a third, the minute there's a cost overrun, they're at your doorstep expecting money, and it's an awfully difficult decision to not give money.
For example, when the gun registry was only supposed to cost a few million dollars, there was a contract to provide it. Of course, they came back and asked for more. And that's how things spiral out of control.