There should be fast food near Cherry Hill campground.
As for downtown, there is fast food. Just a few blocks north of the mall is tons of office space, so there is plenty of lunch places. McDs, BK for sure. There's a Chipotle by the verizon center, but it always has a long line. There will also be a ton of places for quick service, either deli-type or with a theme like chinese, salads, pizza, etc.
I find eating lunch in DC comparable to eating at Disney. Figure an adult lunch will run around $10, with drink. Most value meals at a fast food chain are a dollar or so more.
So much of what's available will depend on where you are tourning each day. The zoo has fast-food type food on site, lots of local quick service down the street. There are a few food courts around, but it's not all that easy to pop around from one part of town to another.