Go ahead and reseed, but understand that the best time to attack crab grass is in the spring, before it comes up, with a pre-emergence fertilizer. It's a safe bet that you won't be able to solve your crab grass problem in one year. But reseeding now with perhaps a little top-dressing if necessary will start new grass which can continue to fill in next spring when the crab grass is having difficulty because of the pre-emergence. Broad-leaf weed killer in the late spring or early summer and a regular schedule of fertilizing, watering when necessary, mowing and attention will eventually produce the lawn you might hope for. But it will take time. None of this happens overnight, and usually not in one season.
And remember, stop paying attention to it for even a half a season, and you'll be amazed how fast the weeds come right back. A manicured lawn with no weeds and no crab grass is a hole in the ground into which we throw money. But, like lemmings, we all do it. Go figure.