I vaguely remember hearing about this in the past. There is not a lot of good information on this. Here is my interpretation from looking around the web in response to your post.
This is a result of the REAL ID program. At some point they plan to stop accepting ID's that are non-compliant (like yours) This program has been plagued with delays and keeps getting pushed back. It's scheduled to go into effect in January but many states are not complying so if I had to make a guess I'd say they'll push back the implementation deadline again.
According to Wikipedia you won't have to show a REAL ID until later:
http://en.wikipedia.org/wiki/REAL_ID_Act
People born on or after December 1, 1964, will have to obtain a REAL ID by December 1, 2014. Those born before December 1, 1964, will have until December 1, 2017 to obtain their REAL ID
Here appears to be the details:
http://www.uscis.gov/ilink/docView/FR/HTML/FR/0-0-0-1/0-0-0-145991/0-0-0-165820/0-0-0-176819.html
It doesn't say you can't travel but it says: Citizens in this category will likely encounter significant travel delays. (but again, I don't think it will be in effect for travel next year).
So long as you cooperate with the security screeners you should be able to get through even if you lost your ID but having more ID helps. I also found some old info on ID (may be out of date):
TSA Contact Center Frequently Asked Questions
Q. If I lose my ID during travel, what secondary forms of ID will be accepted?
A. Passengers who do not have a valid photo ID, such as State-issued drivers license, should bring any ID or documents they have available to assist in verification of identity. Passengers need at least two alternate forms of identification, such as a social security card, birth certificate, marriage license, or credit card. The documents must bear the name of the passenger. Also, one of these documents must bear identification information containing one of the following: date of birth, gender, address, or photo. If TSA can confirm the passengers identity, they may enter the secured area, but they could be subject to additional screening.
If it were me I would just go ahead and sign up for the REAL ID Drivers License that will be good now and into the future for travel through airport checkpoints. When they finally get around to restricting access to checkpoints via REAL ID you'll be glad you have it.