Ok, I had made a whole huge zoo to try this out, and it does work. I had a first generation jaguar give birth to 3 cubs (1 then 2). I wonder if you could keep on doing it and get like 9(although that might be pretty challenging). I'm 90% sure this works with all animals. What you have to do is put the mother in the very small cage(i'm not even sure if it has to be small), and pause it right when you see the babies popping up into the world. If the mother's status still says "giving birth", it should work, hopefully. Pick her up and put her in another exhibit, and she will give birth all over again. And, wa-la. You have some pretty nice sized litters. :lol
EDIT: Ok, I just went back to experiment with my theory of getting as many babies as possible. I repeated this process of putting the mother in different exhibits until she had 6 babies! :w00t So, it seems it may be possible to get as many babies as you want!
Oh, the excitement.
EDIT: Ok, I know, another edit, but I just had 3 births with Cheetahs and every time when the mom finally had a set of two babies, I couldn't use this cheat to get more babies.