When you say 'no debt' do you mean zero? Or minimal? Lenders look for debts being paid on time, over long periods. If you have no or minimal credit history, you're gonna have trouble getting a loan even with 20%+ down.

I made less than 35k a year and was 40k in debt, but I had lenders calling me to sign me up for home purchase, simply because my CC and other bills were paid on time for several years. Almost bought a house with zero down payment, but it got snatched up by an 'investor' that paid cash while my paperwork was being processed.