Clearly, it is possible. You would need a couple of strong developers and a great designer to get things rolling. Game play design is key in the case of Minecraft and GUI in the case of Angry Birds. If you want to really do well, that is going to be hard. I like this article about the Physics of Angry Birds. These games work well, and the subtle details make them really shine.
There was an interesting article in Business Week about iPhone Apps a while back. A maker of a shotgun noise app claims to have made $1M in ad sales. Wow.
Maybe it would be better to work on games, instead of a national website and service company? Higher margins, some possibility of success?
Anyone ready to jump in the pool and write a game?