There are several states (Virginia is one) that has state bond programs that are used in conjunction w/ FHA loan programs. Many FHA lenders have what they call a FHA/VHDA loan that will go to 102% (97% first, 5% second for closing and down payment). The second meets HUDs criteria. Seller can pay points. It also allows for a family of 2 to have an income of 100K or so, and a max sales price of 408K. The only cash requirement is the buyers have 1% - they don't have to spend it, they just have to have it. UW is FHA driven. First time buyers (3 yrs).
Many mortgage brokers avoid state bond programs because income is limited and the loans can be labor intensive (especially if you have never done one). I would look into your state's housing programs and at least know what you are up against if you can't/won't do them. I use to avoid them like the plague, now I am quite well versed in them. If you would have told me that this time last year, I would have said you were crazy.