You may want to look at staying at a hostel instead. Here is a link.http://www.hostels.com/us.dc.html
Hi , Well interstin that you are going in a group . You can go for cheap hotels bookings, that suits you and within your pocket reach and far better you are planning to go isn this season as most of the travel portal give good offers and discounts Now . Well I know such one it is cheap , I have made lots of bookings from there and iot is trustworthy site with loads of discounts . Try this one out http://www.hotels2stay.net/washington-dc��
there are quite a few sites that you can search that will likely show you great hotels at the best prices available. check out the website BookMe and you will be able to compare prices on all the reputable travel sites in just a couple minutes. it s very convenient and will save you a bunch of time and money. Also, make sure you buy them online... otherwise they charge much higher fees for phone orders. good luck.