Yes, you can get away with a 3% down payment with an FHA loan. But 3% is still $6K on a $200K property, even more if you're trying for a $250K or $300K property. That doesn't include closing costs, nor an emergency fund you need for homeowner expenses that traditionally come up.
Sure, you can afford the house at closing. Are you financially well off enough to afford it for the next 15/30 years (depending on loan term) so as to not lose your equity?
Probably not, and that's not going to get fixed until incomes start rising.