I would strongly advise that anyone not give sensitive documents such as birth certificates or SSN cards to TSA employees. If one does not have a passport card (what I use), passport, drivers license etc., the TSA employees will just ask a series of questions and compare your answers to publicly available databases to confirm your identity. Anecdotal evidence has shown this can take as little as 15 minutes.
A passport card is the preferred choice of ID, since it has the least amount of personally identifiable information on it.