I didn't think you could fly without an ID, but according to this 2013 TSA blog post, you won't necessarily be turned back.
You’ll be able to fly as long as you provide us with some information that will help us determine you are who you say you are.
If you’re willing to provide some additional information, we have other means of substantiating your identity, such as using publicly available databases. If we can confirm your identity, you’ll be cleared to go through security, and you may or may not have to go through some additional screening.
If we can’t confirm your identity with the information you provide or you’re not willing to provide us with the information to help us make a determination, you may not be able to fly.