It would work by a couple of mechanisms.
1) because as illegals gain experience, connections and knowledge about how to move up the employment ladder (while continuing to accept wages and living conditions below what Americans and legal residents would, and while people like Bush continue to sit on their hands), illegals gradually move into those rungs.
In the past, only workers doing the most menial jobs would have to worry about wage depression from illegal labor. Now it's basically anyone in any trade you can think of.
2) People who can no longer, due to wage depression, work doing jobs that illegals have taken over have to move into a field in which the illegals haven't. That means there are more people in that field competing for those jobs, which means wages go down in that field.
On the other hand, their presence has kept agricultural wages low. If all the Mexicans disappeared, farmers might have to pay $25 an hour to get Americans to pick strawberries.