When I started development on scribophile.com I was in college and working part-time. I had maybe $5000 in the bank. My big financial risk was paying a freelance graphic designer $100 for a few FB-like gift illustrations and laying down $500 in Adwords spend for the first month after launch. After a few months it was paying for itself and had returned my small investment, and it's been growing ever since then. Nowadays I have significantly more in the bank, but developing and launching the site was practically free (besides sunk time costs).

If you want to do your own project full-time, make an estimate as to how much it costs for you to live in your area per month. $1000? $2000? It's hard to say because it will depend on where you live. Set aside 12 months worth of cash (6 months for dev time and 6 months to give yourself some time to make money after launch) and maybe a little extra for emergencies, and get to work!

Of course this is assuming you think you can become ramen-profitable in 6 months. Many people haven't become ramen-profitable in years, or ever. It depends on what your living expenses are and how you are monetizing your project.