It could also possibly be the generation after the six day war in 1963, I believe. I read that 'theory' once myself. We'll soon know, I think.
I think its the generation that begins to see the signs that relate to the end, about which Jesus was talking in Mt 24 and Lu 21.
1968, not 63, and we are already beyond the 40 year generation, since the "secret rapture" needs to happen seven years prior to the end date of the generation.
We should already be well into the "great tribulation". The revived Roman Empire should be up and functioning. Millions of Jews should be lying dead in the cities of Israel. The antichrist should be sitting on a throne on Jerusalem and the one-world goverment should be in place.
All this makes perfect sense if you are into pure speculation. But in reality we are no closer to any of these things from a sensory standpoint than we were in 1998, or 1968, or 1948. It all remains a mystery to the literalists and carnal interpreters of the Word of God.