April 1, 2007 is the 91st day in the Gregorian Calendar, with 274 days remaining.
(Jane and Jesse are walking back to the booth, sodas in hand) Jane - You see, my theory is that our primitive hunting instinct has no outlet in modern society. Jesse - Cool. (slurps soda) Jane - So, rather than stalking animals, we substitute it with the shopping experience, and hunt for objects. Jesse - Cool. (slurps soda) Jane - (exasperated) And then, Jesse, while we're asleep, those objects come to life and plot their secret take over our civilization. April 1st, 2007. That's the day they make their move! Jesse - Cool. (slurps soda)
Clearly, Jane is trying to determine if Jesse is paying attention to her, and he clearly isn't. As this episode was first aired on March 16, 1998, the imaginary peril was a good nine years away.
When April 1, 2007 actually arrived, Daria fans joked about either being attacked by inanimate objects, or joked about somehow escaping the peril. April 1, 2007 came and went more or less without fanfare.
However, the statement of a particular date unfortunately dates the episode, leaving future fans the task of explaining the anachronism.
Civanfan wrote an untitled fanfic that played the concept straight and explained how Jane knew about it.