The Administration probably leaked this to Republicans basically threatening that if they don't come to the table and negotiate in good faith, they'll move on this by themselves.

I think the "move to 1996" statement means they can move the amnesty date enacted in the 1986 immigration law from 1972 to 1996. I don't think they can go beyond 1996 because 1996 was the year the 1996 immigration law was enacted.