Of course, the dirty little secret is that rich, white conservatives also hire and/or benefit from the hiring of illegals. How many rich conservatives check whether their maid, nanny or gardener is here illegally? How many conservative meat-packing plant owners, construction contractors, landscapers etc. check their employees' papers?
Illegal immigration is a lot like illegal drugs: you'll never end either of them by targetting the supply. Only when the demand goes away will the supply dwindle. Certainly, border control is important, but the best way to deal with illegal immigration is to start enforcing the laws against hiring illegals.
Target the big companies that hire illegals and stick them with massive fines (IIRC, you can get up to $10,000 in fines for each illegal you knowingly hire). Start going after regular Americans who knowingly hire illegals- that illegal nanny stops being such a good deal if you have to pay a $10 K fine for hiring her.