That is one argument. Let me pose another.
Bush knows that 30000 to 50000 operatives from the middle east have jumped the Mexican border. He also knows an attack from them is imminent. If the attack happens before amnesty is passed, there will be no amnesty. Therefore, he needs to pass this bill now before the excrement hits the fan.
That is the most logical thing I have heard proposed on the "why" issue in quite some time.
Even if provisional “Z-visas” are given to all of the illegals after the bill is passed, they would probably be revoked by law, due to public outrage if a major terrorist attack is traced to covert jihadists blending in with illegal aliens.