According to this letter to Senator Warner of Virginia, dated August 2, 2007 the TSA claims it has Authority to Require ID.
http://www.dubfire.net/warner-tsa.pdf
"....(passenger) asks whether TSA may require a passenger to produce a form of identification, such as a Federal or State government issued ID, in order to fly domestically,
TSA has Statutory authority to establish such a requirement. To date, TSA has no implemented this authority."
