They may still let you fly if they can prove your identity.
https://www.tsa.gov/travel/security-screening/identification
In the event you arrive at the airport without valid identification, because it is lost or at home, you may still be allowed to fly. The TSA officer may ask you to complete an identity verification process which includes collecting information such as your name, current address, and other personal information to confirm your identity. If your identity is confirmed, you will be allowed to enter the screening checkpoint. You may be subject to additional screening, to include a patdown and screening of carry-on property.
You will not be allowed to enter the security checkpoint if your identity cannot be confirmed, you chose to not provide proper identification or you decline to cooperate with the identity verification process.
Thanks.