What equipment do your flights use? If you're making a mainline to mainline connection, you'll have a much shorter walk than if you're making a mainline to regional connection.

Your wife is partially right... DL sold you your ticket, so they will get you from DEN to DCA. However, if you miss your connection to the last flight of the night, there's not a thing they can do other than rebook you the next morning. If the delay is due to something outside their control, like weather, they won't pay for your hotel for the night (though they will if the delay was within their control, such as mechanical).

DL sold you a connection it deems to be valid, and will get you all the way from DEN-DCA. That said, there's not a whole lot of margin. A scant 15-20 minute delay or a seat in the back of the plane and you're in danger. If you absolutely have to be somewhere, a 34 minute connection to the last flight of the night where the next morning's flight arrives too late is a risky bet.