Eminently doable, and you should! But, with just a few hours you really have to be focused on what you want to try to do: 1) a quick spin around to take in all the iconic sights with a couple of brief stops, 2) visit one or two museums for an hour a piece, or 3) an extended visit at a particular museum/sight (as previous poster wrote, any one museum/sight can easily take hours)?

If 1) then the BigBusTour hop-on, hop-off ticket around the Mall might be a good way to go (or, rent an e-bike if weather is nice). Not cheap, but gets you around to all the big sights (Lincoln, Washing Monument, WWII, Vietnam memorials, WH, Capitol, etc). if 2, most of the Smithsonian Museums, esp. the art museums, have a "quick hits" map of the most important/famous items that is very useful. If 3, then pick what interests you most and take your time to get the most of that visit.

DCA is generally very quick to navigate IN-security and get to your gate - it's the smallest big city airport one can imagine. Uber or any street taxi will generally be quickest for getting to/from to the airport - but do keep an eye on traffic reports, things can change quickly and sometimes Metro is quicker.