That would only work if most illegals were making enough money to be paying much in taxes. Most Mexican illegals lowly educated, low skill folks, who are a drain on our resources, and will take far more than they put it, even if they were legalized.
The government doesn't look at it that way. If each worker is a small contributor to FICA, then (under government logic), the country needs MORE of them.
Center for Governmental Studies "Immigration and immigration policy"