I can't imagine TSA would care if your DL was expired -- it is still a valid ID, just not valid to drive with.

That said, you now have to wait for the passport to arrive so no choice but to SDC (same day confirm) to a later flight. Pick a flight you can make, and 3 hours before that flight (for example, if you can make a noon flight, then at 9 am) call in to SMS and ask to SDC to that flight. Must be 3 hours or less before the noon flight. 8:58 won't work. If there are any seats still for sale on the hypothetical noon flight, you can get on it.

If the earliest flight you want isn't available, then you can wait until exactly 3 hours before the next flight that is available and call again.

Worst case, just go to the airport and get boarding pass for the earliest flight available for SDC, then go to the gate for whatever flight is next and ask GA to put you on the standby list.

If you can't get a new flight (because the earliest flight with seats is more than 3 hours away), I think you can get a pass from DL that will let you through TSA so you can go standby for an earlier flight.