Maybe. According to TSA: 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. A 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 will 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 choose to not provide proper identification, or you decline to cooperate with the identity-verification process.