1) I would make sure that illegal employers are fully responsible for all expenses involved with presence of illegal aliens. Many programs like social security have a modest redistributive effect from well-to-do tax payers to those less fortunate. We need to make sure that illegal employers don't take advantage of those kinds of benefits.
Payment of generous benefits doesn't necesarily need to involve continued presence in the US—in fact those benefits can and should be tied to repatriation.
Now we need to make illegal employers legally liable for accidents and crimes involved with the presence of illegal aliens.