Most definitely they do.....just remember, the more items you use on the loan menu, the more expensive the loan.
For example, if you go with a 100%, no PMI, fixed rate loan, you will be paying a rate well above market.
If you can put 5% or even 10% down, you can get a decent rate and still not have to pay PMI.
I personally know of 5 or 6 banks in our area and one credit union that has the program (the credit union is national and anyone can join - I am actually thinking about going to work for them).
They all vary by down payment, interest rate and loan program and current job status. Some accept contracts without even starting the job yet, some want tax returns.