The TSA explicitly allows people to travel without ID. The following is taken from https://www.tsa.gov/travel/security-screening/identification:
In the event you arrive at the airport without valid identification, because it is lost or at home, you may still be allowed to fly. The TSA officer may ask you to complete a form to include your name and current address, and may ask additional questions to confirm your identity. If your identity is confirmed, you will be allowed to enter the screening checkpoint. You may be subject to additional screening.
You will not be allowed to fly if your identity cannot be confirmed, you chose to not provide proper identification or you decline to cooperate with the identity verification process.
TSA recommends you to arrive at least two hours in advance of your flight time to allow ample time for security screening and boarding the aircraft.
As I noted in a comment, I once traveled with someone who did this. She is a US resident (non-immigrant) with no official ID issued by any US entity, and she forgot her passport at home. They checked some of her credit/bank cards (and maybe her work ID, if I recall correctly), and let her fly. I think it took about 10 minutes, maybe 15, to get past the ID check. On the way home, it only took a minute or so extra.
I would therefore recommend that you bring everything you can that has your name on it, including your expired passport. They may reject it because it is expired; the page quoted above does say that the ID must be “valid.” The expired passport may nonetheless lend weight to your claim, and it certainly won’t hurt it.
Also bring bank cards, library cards, employee ID, social security card, birth certificate, school records, anything you can readily get your hand on. The worst possible outcome would be to leave something at home only to be told that you would have been allowed to board if you had brought it.
When you approach the ID officer, hand your boarding pass and say something like “I’m afraid I don’t have any valid ID, but I do have this expired passport and these other documents.”
If you are sensitive about being scolded, and worried what they might say, you can bring a printed copy of the TSA page that explains that ID isn’t strictly necessary.