LORELAI: Now comes the reason for my phone call.
CHRISTOPHER: All your regular 976 numbers are busy.
976 numbers are premium phone numbers on a local level, as opposed to 900 numbers, which are national. Calling such a number will charge you by the minute. They were first used in the early 1970s. Although premium numbers could be used for such things as the time or the weather, they were especially associated with adult entertainment lines, which is what Christopher is implying.
Although the internet has almost killed off the old-fashioned sex line, they are still gamely struggling along.