And here is where movie lore gets messed up.
According to T2: Judgement Day, the first mention of the date for Judgement Day is August 29, 1997. 2:14 am eastern time, to be exact. In Terminator 3, on the DVD, there is a timline which states the date is in 2003. In the TV show, it is said that the date is April 29th, 2011.
So, we have already passed several Judgment Days. I can't wait for Google.. err.. Skynet to become self-aware and start the war.