If this is a domestic trip -- and presuming you are not on a no-fly list, can do self-check-in and have only carry-on luggage -- then you can definitely fly but will be subject to additional security screening at the airport security checkpoint to get airside.

Odds are that you will have no problem with the airline, because the check-in rep rarely look at DL expiration dates.

Odds are that the TSA will make an issue of your expired DL, but all the TSA can do for a failure to present ID -- when you have a valid boarding pass -- is to send you to secondary screening of the sort that haraSSSSment-selectees are subjected to at the airport security checkpoint to get airside.

I would not worry about it, since this is something that the airlines and TSA see quite often during domestic travels.