Tim has this one spot on.
Genesis 6:1-8
1) When men began to increase in number on the earth and daughters were born to them,
2) the sons of God saw that the daughters of men were beautiful, and they married any of them they chose.
3) Then the LORD said, "My Spirit will not contend with man forever, for he is mortal; his days will be a hundred and twenty years."
4) The Nephilim were on the earth in those daysâ€â€and also afterwardâ€â€when the sons of God went to the daughters of men and had children by them. They were the heroes of old, men of renown.
5) The LORD saw how great man's wickedness on the earth had become, and that every inclination of the thoughts of his heart was only evil all the time.
6) The LORD was grieved that he had made man on the earth, and his heart was filled with pain.
7) So the LORD said, "I will wipe mankind, whom I have created, from the face of the earthâ€â€men and animals, and creatures that move along the ground, and birds of the airâ€â€for I am grieved that I have made them."
8) But Noah found favor in the eyes of the LORD.
God was so grieved at what was going on, He decided to wipe out the world in 120 years, and kill everyone and everything, but decided to spare Noah and his family. Whether God made a decision about Noah before or after He decided to destroy the world is unclear; a literal reading of the text would lead one to believe that the decision came after His decision to destroy the world.
In any case, the 120 year limit was on how long mankind had on Earth before the flood was to come, not a cap on the lifespan of each individual human.