It would just depend on your comfort level with all the variables (both tangible and intangible).
I like my day job quite a bit and am not really looking to quit, but have asked myself the same questions you are asking yourself. Below are the basic criteria I would need:
1) enough money to comfortabley live for about 8 to 12 months doing nothing at all.
2) enough money IN ADDITION to number 1 and access to enough credit to persue enough and sufficiently large deals to generate at least what I NEED and enough more to conduct more deals and acquire rentals along the way.
3) I would need to have completed about 3, maybe 4 deals successfuly and with sufficient profit to prove to myself it is possible and that I can do it.
4) Not necessary, but ideally I would already have 3 or 4 rental propeties with good cash flow just to add some (relative) stability. Of course, my long term goal would be to add to that number.
Based on what *I* am comfortable with, it would probably take *me* about 5 to 10 years of working realestate very hard as a second job before I accomplished enough to justify quitting my day job. But, like I said, I enjoy my day job and it a career, not a J.O.B.
I am always curious about how others do it (whether in real estate, business or anything of substantial success). I am always interested in successful people's stories. I have yet to hear one story that did not have some sort of stroke of luck that the teller was fortunate enough to capitize on. I think we are all blessed with multiple strokes of luck throughout our lives. But how, and if you capitalize on that grace shapes the unique outcome of your story. Being open minded and flexible is the key.