In fact, to get to DCA on UA, you'll HAVE to do as Shadow suggests.

Another (probably lower cost) alternative is to fly xxx-IAD-BWI on United Express (Atlantic Coast). Advantage: you won't be tempted to upgrade the short flights since you'll be on puddle-jumpers. And the 500 miles you get for the 15 minute IAD-BWI is one of the best miles/minute deal around! Disadvantage: you'll end up in Baltimore, not Washington and service on ACA pretty much sucks .