I think your standards may be too high. Elian Gonzales and Terri Shiavo both had a cultural impact...a big one. To brush these stories off as events that "come and go" with the likes of paparazzi stories of Hugh Grant's prostitute is troubling.
What exactly does a film need to do for you to agree it has had a cultural impact? Avatar has transformed the 3D film from a gimmick to an viable, profit-making tool for films in the future. If you are waiting for a new powerhouse religion to emerge from a film's impact then you will be waiting a long time, these are only movies after all. By your standards even Star Wars has not had a cultural impact, because beyond people "knowing about it," albeit for a long time, what else is there? No worldwide powerhouse Jedi religion basking at the greatness of the savior, Mark Hamil.
Star Wars has had a significant cultural impact, and so has Avatar up to this point. Like I said, it is only debatable if you want a film to bring about nirvana across the world before it has a cultural impact. Besides that, I first brought up cultural phenomenon, not impact. Something that has taken the world by storm. Like it or not, Avatar has done this, as has Twilight and Titanic. If you want to debate the longevity of Avatar's impact, that is another story.
I think that defining something as having a "cultural impact" implies a longevity of effect. Star Wars did have this effect that I'm talking about, but we only know this looking back on it. Terri Shiavo similarly had an effect, a massive effect, but it came and went and the only possible repercussions are that some ********* politicians who tried to capitalize on it were thrown out of office come next election. Do people still frequently think about it? Does it pervade the public consciousness somehow? Has it shifted our nation's priorities regarding issues of life and death for people who are on a breathing machine? I don't think so. Every year we probably get 20-30 cases that make the headlines for awhile and are forgotten about. Until I see a real reason to think otherwise, I am going to assume that Avatar is in this boat.
To me, this is like claiming that a U.S. President is "great" without historical hindsight. You don't know how great someone is until you have had a chance to move away from it.