Recently flew with a friend of mine. She has a permanent resident card, but no driver's license (lives in NYC). She often travels in US airports with that card and a "Reentry Permit" (sort of a passport, but white) for backup. She was originally from Latvia (soviet days), and moved here as a child. Usually she has not had a problem showing ID checkers her Permanent resident card, however with some airlines employing private ID checkers, they often have no idea about the proper ID requirements.

At JFK, I flew Jetblue on their Shuttle route to Boston (great alternative to US by the way) with her. At security, the Jetblue employee before TSA had no idea what the card was. It was the new post-9/11 redesigned version with holograms, and other security features. The ID checker looked at it as if she was seeing an Alien.
First, she said this wasn't valid "government issued identification" (other than the fact that it says Department of Homeland Security, Permanent resident card, etc). Then she accused it of being fake (it was recently redesigned). Then she said Latvia wasn't a country. After this, I got upset and asked for her supervisior. The supersivor and the ID checker dissapeared with the card for 5 mins (probably checking the big book of ID's) and said they would let her through with it "this one time." Meanwhile, as I got pulled aside for secondary, I was telling the TSA screener about this and she laughed saying that "the ID checkers make us look like Nobel Laureates" and that "they have even thought out-of-state Driver's licenses were fake because some states print them vertically."

If you ask me, I'd feel safer with the TSA runing the show rather than high-school dropouts.