By "annihilationism" I think you mean the idea that God destroys souls which do not make it into heaven, rather than letting them suffer eternal torment in hell.
If one is going to make an argument for annihilationism, it would have to be from concepts in the Bible rather than specific pieces of informatiion. There are theologians who support the annihilation of souls, arguing that this is God's mercy, and that if "God is love," then He could not be comfortable with human beings suffering forever with no chance at release. C.S. lewis made some case in The Great Divorce" for annihilation when he said that heaven tries to help damned souls, but at some point it is just like blowing dust in your own eyes, and they would at last sweep the dust up.
In Revelation the fiery lake is described as being "made for the devil and his angels," and some take this to mean that it is not for humans. Since everyone knows many also reject Christ (at least in this life), where would souls go who can't get into heaven, and yet don't belong in hell? Annihilation is one answer.
It's my impression that annihilation is not a very popular doctrine, but i know it is out there.