So, I screwed up, and put too much turf fertilizer on my lawn. It's not completely brown/dead, but there are some pretty significant patches. Is there any way to recover from this? Or is my only option to till the soil and put down new seed?
If it's not totally dead you can try to water it back to health. You should at the very least try this first. Grass is normally pretty hardy and it might survive if you clear the soil of fertilizer.
If it's dead and gone soak the area a few times to try and wash out most of the fertilizer and put some patch seed down. This is the stuff that has the fibers with it to make sure it's not just barren seed on the ground. You could also just put seed down.
If it's the entire yard, you might look into getting it hydro seeded.
In any event nothing is going to continue to grow if it's overly saturated with fertilizer. Fix this first, and then the grass. Water run-off is bad for the rivers and nearby ponds but nothing much can be done about it at this point.