DC at spring break time is always absolutely insane. Regardless of when DC schools are out, every middle school in the country seems to take field trips to DC over spring break! Where I work used to be in Crystal City before the base realignment process. From about this time of year through the end of April, there were always hoards of teens in the food court area, because that was how their packages were set up.
Even with that little rant, DC is a really good place to visit. Sometimes you can see cherry blossoms in mid-March (probably not this year cause it's been pretty chilly), and the temps are usually reasonable at that time. You'll probably need light jackets and be prepared for the occasional shower, but at least it's not 100 degrees with 98% humidity like the summer here.
Oh, and to answer your original question, our kids get between 2 and 4 days off for spring break (depending on snow days, they can take back the first and last day). This year, they are off 8-13 April (yes, that's Thursday through Tuesday, I know it's weird!). Catholic schools are off the from Good Friday through the following week.
Good luck!