Many of the jobs occupied by illegal immigrants are not desired by legal citizens. The article mentions that the only population these jobs are affecting are the high school drop outs who desire the same jobs. Many of the illegal immigrants do not pay taxes but still take part in many government programs funded by these taxes. Would this distort the supply and demand of these government programs?
If you removed all of the illegal immigrants out of the three major cities you would see an increase in wages almost immediately. But shortly after you would get a large supply of employees moving to that area for higher paying wages and it would bring the equilibrium of wages down once again. So the overall impact of illegal immigrants to the job market is very minimal if any in most areas.