Parking is always a problem at DCA. They are building more space but it will still be a problem. And if your taking an early flight out and figure "I'll just stay overnight at a hotel", that parking will be $40-$50 per night.
Solution ... park at the Huntington Metro garage. There's plenty of space and you only pay for 1 day ... the day you leave. From the Metro, you can either take the train for a 15 minute ride to the airport, or just Uber to the hotel for the night. I Uber to the hotel, then upon return, use the train to go south to pickup my car. And even if you arrive when the trains aren't running, the garage is always open so you just Uber out.