The topic says it all. I am wondering how likely it is to become an indie game developer and make sufficient money to pay rent, food, internet connection etc...
Very unlikely... I'm sure that some minor googling will unearth a ton of horror stories from people that tried exactly that, and failed miserably.
Will you fail too? Not necesarily, but it is a major gamble, and not something you should think of lightly. As with any private business, you better make sure you have all your ducks in a row: have a solid business plan, realistic expecations, and be prepared to work your behind off. (That's all assuming you do indeed have what it takes, and can consistently create 'fun', high quality games)
Keep in mind that even if you are successful it will still take a significant time before your investments (time, effort, money) will pay off -- so think long and hard before quitting your job chasing this dream -- more than likely, you'll depend on it to pay your rent, food, internet, etc. for a considerable time.
However, if you ARE seriously committed to making this work, you could look into how much money you actually need to make ends meet, and see what you can do with that. Maybe you can switch to a part-time job, making just enough money to pay your way while also freeing up additional time to dedicate to your programming endeavours... Personally I'd try to get a good head start on things while having a full-time job on the site though -- have a steady, reliable income, and possibly also be able to put money to the side for when you need if you DO take the plunge later on.
Just keep realistic, and consider the worst-case scenarios as well. Like they say, most business fail in their first year of operation... and I have a gut feeling that that percentage is conssiderably higher among indie game creators.