I was working with a similar setup and it wasn't that bad at all. We knew what to expect, and somehow we felt that our work has a purpose, because we needed the money at that time.
Unfortunately, when one brings up the money based motivation topic up, the other immediately pulls Daniel Pink's book, which is excellent book, but how one interprets is very important. Dan doesn't say that the money based motivation is evil, he simply proves with scientific methods that it is not effective with knowledge workers under certain circumstances.
The book mostly talks about cases when something has to be done, and the leader needs to motivate people to reach a certain deadline or threshold. In those cases the money serves as a short term motivator, which takes away the focus from the joy of the work etc.
The title of the doesn't say anything about money: "Drive: The Surprising Truth About What Motivates Us", because it is about motivation. If you agree with people in the beginning about the rules, then this is not a case of motivation. This is how business is going to be done. If you start being behind the deadlines and commitments and you offer money that is a money based motivation situation.
My point is that you should talk bring this topic up, and talk through with your colleagues and learn as much as possible about their motivations. If it turns out that none of them is interested in money, you can do practically anything and nothing is going to change.
To sum up: use as much time as necessary to figure out what motivates your colleagues and change the rules accordingly. Don't assume anything, do your research.