OP, are you interested in living in the city itself or a suburb?
Like several of the other posters, I grew up here (in a NoVA suburb), so the crazy COL always seemed normal to me. I moved into DC after college and lived the dirt poor nonprofit worker lifestyle. I love living in the city, and my now-DH and I decided early on that it was worth the trade offs. He makes about $125K. I was only making about $45K (again, nonprofit), and I became a SAHM after we had a child. You really have to know what sort of trade offs you are willing to make? We live in a 2 bedroom, 1,000 SF condo. We don't have a yard, but on the other hand there are tons of kids and parks around us, and with less than a 5 minute walk to the metro (and we only have 1 car), we pretty much consider the whole city to be our backyard. Even without the metro we can walk to the zoo, library, grocery shopping, 5 or 6 playgrounds and parks, and about 200 restaurants. Our condo is not fancy and our local school is average, but we love our fun, walkable neighborhood, and DS spends his days having fun at museums, parks, the zoo, etc. By DC standards we don't make a lot of money, but we love our lifestyle.
What is comes down to, OP, is what sort of lifestyle do you and your family want? What are your non-negotiables? What are you willing to sacrifice?
Btw, don't listen to the snarkers who hate living here. No place is perfect of course, but DC is a great place to live if you are looking for that lifestyle.