I think the game either should have some kind of end game condition instead of that 02:00 AM time freeze (It's really feel like a bug even if it's design decision)
Or the game should give you other options that will inflict some kind of penalties if you do not manage to get the money.
Looks strange to me that you can decide to be a Hobocop, but not sleep on a bench or something similar.

I was trying to role play a character that will not take bribes, beg or steal anything that is not nailed and that got me locked second night. I used all the relatively honest ways to get money to pay for the first night.
It's a shame, I fell so much freedom in everything else in that game.
I have to replay the whole second day in order let Kim sell his awesome rims for me the first night. At least was touchy moment :-)

The game is awesome I don't mind to much to have to replay the whole day, but still I think that this is one aspect that the game can improve. :-)