Try Jubilee Jumpstart in Adams Morgan, and there’s one called David’s Stars (I think?) in Dupont/AM. Also maybe First Baptist Church on 16th. You should be able to get a list of licensed, registered centers from the DC Dept of Health–this one is from 2007 but I have a vague recollection of being told that the DOH maintains a more current list that you can go down and pick up. http://hrla.doh.dc.gov/hrla/lib/hrla/pdf/null_report_child_development_homes.pdf
Your best bet might be a nanny share–they seem to come together pretty quickly. Definitely send an email to any neighborhood listserve you can find–there’s a Petworth Parents group and I’ve often seen nanny share openings there. We also had fairly decent responses to posting an ad on SitterCity for occasionally babysitting and they do nanny listings too. Most of them were asking $12-18/hour, though, so that will add up fast.
Lastly, I have a friend who used to nanny part-time and just had a second baby a month ago. I have no idea if she’s looking to take on some work and she does have two kids of her own, but she’s awesome with kids and might be willing to help out in a pinch. I could put you in touch with her if you’re really stuck. I actually suspect that you and I have met–if you were offered a baby swing by some random person who works in the office building next door, then email or give me a call if you still have my info and I’ll put you in touch with my friend.
Good luck. You’ll find something; everyone does!