That looks like what is taking over my lawn in western North Carolina. I think I've identified it as alligator weed, which seems primarily known as an invasive in waterways. It has formed a dense, boggy mat in the lawn. I don't want to use chemicals, but pulling it out by hand is really a chore. The roots are tenacious. Would love any tips for how to eradicate it!

I'm not sure what it is, but it looks like you have enough of it that you can just spray it all with glyphosate and start over. Get on a good pre-emergent program next spring to keep it from coming back.

http://lawniac.com/conquering-crabgrass-and-annual-weeds