Source: http://www.irs.gov/taxtopics/tc152.html
The other thing to know is that e-filed tax returns are subject to an immediate sanity check (i.e., has this ssn already been used?, is this a valid zip code?), which doesn't exist for paper forms.
How much would your answer change if you found out that there are only two people processing paper returns? 2^32 people? What if you found out that the types of returns that are mailed in are 10x more complicated/detailed than e-filed returns? Would it change if you knew there was an intentional processing delay on paper returns to increase e-file adoption?
For me, personally, it was 7 business days this year, and I did the filing in all of an hour and a half, in an afternoon. And that includes the time spent trying out two other free apps to decide which ones I liked better.