The only explanation I've seen is that it refers to a to the red-light district of a town. If a particularly rowdy gang continued their carousing outside the confines of the red-light area it was considered that the whole town was being painted red. It's an American phrase originally.
The phrase originated when Melton Mowbray in Leicestershsire was literally painted red by some of the sons of aristocracy staying at a stately home in the area during the C18th. I am sure more details will be found on a tourist site for Melton Mowbray.