When the weather is warm, I typically quarter my deer the same day it's shot or the following day. I place it in a large cooler with three gallon sized jugs of ice, which I rotate with another set of three jugs. I leave a grate in the bottom to allow the blood to collect below the meat. I usually keep it in the cooler between four to seven days, depending on when I have time to cut it up. I know I've gone as long as 10 days. Never had an issue.
Mike