I've been in your shoes. Before I Rent a Coder was big enough to support me full-time, I had to find a way to smoothly transition from my stable full-time job, without causing myself a coronary. ;-)
I took the tactic of working a full-time job to support myself, and then coming home at night and then working on my start up another 6 to 7 hours. This isn't the strategy for everyone since some people have family and other commitments that prohibited. But if you are single like I was, it is the safest way to make the transition, because you are never without an income. This can be crucial if there are problems with your business plan (which is almost always the case) and it takes longer to create a sustainable business than you first anticipated.
Here's another tip: when Rent a Coder was finally doing well enough to support myself, I told my boss about it in my intention to work on a full-time. Since I had done a good job for him, he offered to let me work part-time and taper off my hours over time as the business took off. This gave me additional income to feed into the business when it was still very new and fragile, and gave me more confidence in making the transition successfully.
Best of luck to you with making the transition and if you need any advice, you can look me up here on clarity.