No one is required to prove that he is licensed to drive, registered to vote, or a student at a university, or to present any documentation of his identity to TSA at airports. Although TSA keeps most of the rules it requires passengers to follow secret, the policy seems to be that if you willfully refuse to show your papers, you will be barred from flying, but if you claim that they were misplaced or stolen and and cooperate with an interrogation intended to determine your identity, you will likely be allowed to fly.
As of today, TSA's own Web site
states:
Cooperative passengers without ID may be subjected to additional screening protocols, including enhanced physical screening, enhanced carry-on and/or checked baggage screening, interviews with behavior detection or law enforcement officers and other measures.
For more on this, see the following FT threads: