First of all, I didn't call them invaders --- although now that you raise that question, I'll have to examine it.  

Your second point --- that we employ illegal aliens --- is largely MY point.  The leading scholar on illegal immigration, Harvard economist George Borjas, says that "The immigration surplus of $35 billion comes from REDUCING THE WAGES of natives in COMPETITION WITH IMMIGRANTS by an estimated $402 BILLION a year, while increasing profits or the incomes of users of immigrants by an estimated $437 billion."  He goes on to say that although the net impact on native Americans is small, the wage losses suffered by some natives are substantial.  “Some groups of workers face a great deal of competition from immigrants. These workers are primarily, but by no means exclusively, at the bottom end of the skill distribution, doing low-wage jobs that require modest levels of education. Such workers make up a significant share of the nation’s working poor.” We are hurting our own poor.