The movie was filmed in 1998. One immediate pop culture reference in the movie is George Bush Sr. giving a press conference and speaking the phrase "this agression will not stand..." referring to Iraq's brief invasion of Kuwait. In this same scene, The Dude writes a check for $0.69 to pay for his milk at Ralphs. If you look closely, the check seems to be dated 9/11.
Given that the actual George Bush coverage was from 1991, one could deduce the supposed date for this scene is 9/11 '91 or 9/11 1991 depending on your whole brevity preference.
Either way, that's enough 9s and 1s to keep the average American confused.