The phonecall could be directed at an ex, or at someone you find unattractive when sober.
Origin: Unknown, but probably entered the mainstream from the film 'Sideways'.
Ugly-chick or Ex-Girlfriend: "Ooh, it's about time you called me, big-boy. Wait... Are you drunk? Oh, I don't care. I'll be down in 15 minutes."
Todd (Lionel's friend): "What the hell are you calling HER for? She's the ex you dumped because she only shaved her legs in the spots where she had holes in her jeans! Did you drink and dial?"
Friend2: Are you drunk?
Friend2: I told you not to Drink and Dial. Your such a fuckin idiot.