No, you do not need to put down 20% on new construction. I just sold one for 5% down. Based on your other question. You won't qualify for a a loan. If you are having one built just for you, then yes you will need more down. First you need to work on your credit & save more money.
Call me & I can give you a better idea of what you need.
Builders and their site agents are not lenders. What you will qualify for depends more on your credit and other qualifications than on what you buy. Meet with a local mortgage broker to get pre-approved and discuss your options.
Best of luck,
Real Estate One Troy