My experience with short-budget and time-limited projects is that you have to sacrifice the quality of the final product up to an acceptable limit.
Typical scenario is that unfortunately the vendor has agreed a prize that may cover your required amount of hours to develop the project but the deadline is not so far. Adding manpower is no solution since projects must mature in some way and, beyond certain point, adding extra analysts and programmers will increase management and coordination effort and not ease development.
There is also a Law you should always follow: do NEVER believe your manager when he or she says: "I trust you; I know you can do it great, so you don't need that much time to test and debug". Just don't buy that.