I wrote a post at 10,000 birds that starts to explore this question by comparing the number of birds that there are, the number of birds that seem to die off every year, and the possible number that get munched by cats, and briefly discusses predator niches and that sort of thing. I hope this is the start of an interesting discussion that will eventually get us tilting at windmills.
Have a look: Are there so many birds that cats don’t matter?