Most of my bows are, according to most people, very short. I haven't done a whole lot of successful hunting, but all of it has been with bows under 60", and most under 50". It's not so much the power that causes problems, but the accuracy. Short bows are far more dificult to handle and shoot consistantly. If an archer is capable of getting the arrow where he needs to, the arrow will do the job.
I would say that, with properly matched arrows, a bow pulling 40lb@20" should be enough to take a deer.
However, the kill may not be humane if you decide to push the limits. I would not feel comfortable hunting big game with a bow of that size. I personally have hunted with a 43" bow pulling 50lb@24" and a 47" bow pulling 45lb@25" and they worked very well and I would not hesitate to throw an arrow at a deer with them.
In the near future, though, I want to go the opposite extreme and make a replica english warbow to hunt pigs with.
We need to remember that nearly all hunting by native americans was done with bows that were less than five feet long. They
must function well enough to take game or they wouldn't have survived.
Sean