I don't suggest taking your birth certificate, social security card, or marriage license with you.

There's no requirement for you to present any identification documents to TSA, only the requirement that you not assert your right to fly without such identification. It's okay for you to say your ID was misplaced or stolen, just not for you to say, "I'd prefer not to show it to you because I know I'm not required to and it's important for us to maintain our ability to travel without getting permission from our government."

TSA prefers to keep most of their policies secret (presumably so bad people will go ahead and do dangerous things and then get caught) but they have published some information about their airport ID policy that went into effect last summer.

For a great summary of that policy, see this analysis of the policy by Daniel J. Solove, or Bruce Schneier's L.A. Times op-ed.