The simple truth is that you need to line up a long term (9-12 month) freelance contract before you quit your day job.
And you've hit on one of my three top reasons why I would find the transition to full-time freelancer to be tricky. (Right after "I prefer the steady income of a salaried job" and "I'm horrible at selling myself.") Right now I freelance in my spare time. I can put in about 10 hours a week freelancing in addition to my full-time job. This gives me enough time to take on one or two clients without overbooking myself (or winding up with no life because I'm working 24 hours a day).
If I were to go full-time freelancer, I'd need more clients, but I can't take on more while also working at my day-job. So I'd need to rely on a greatly reduced income for a few months until I built up enough clients to match my current salary. Of course, this could take months and months during which we'd fall more and more behind financially.
This isn't to say that it couldn't be done. (If I were ever let go from my job and couldn't find a new one right away, full-time freelance might wind up being my new work-situation.) It's just that, at this point in my life, it is an unlikely and very risky path for me to take.