A few things:
(1) When you move to DC, if you register with a lot of temp agencies, you will get a job pretty quickly. It won't be high paying, but it will be a good way to make some money while you are looking for other jobs, and it will also be a good way to learn about companies in the area. (And if you are entry level, it's a great way to snag a full-time job; a lot of companies love the temp-to-hire route.)
(2) All my jobs I ever got were from networking. Start networking. Go to alumni happy hours, go to happy hours in your profession, or just crash happy hours. It's very, very important. (I actually miss this aspect of DC, because in Denver I don't have a network and it's hard to find something in my field).
(3) You can find decent, cheaper group housing in the city. I highly recommend you go that route. The city is AMAZING and totally fun. You also will either need to ditch your car or, if you insist on having one, make sure it's super cheap and is okay if it gets scratches or broken into.
(4) DC is a GREAT place to go to grad school! I highly recommend it, because the internship opportunities are AMAZING!