Show you that illegal immigration lowers wages? It is basic economics (supply and demand) but if you cannot figure it out I will give you a personal example. When I hired a nanny in the early 1990's, I interviewed several young American citizens who were willing to work for one thousand a month ($12,000 a year, not exactly high pay). At the same time I was offered help in obtaining an illegal immigrant from Guatemala who would work for $400 (without of course Social security or unemployment taxes). When I asked them what they would do if their nanny who they brought from Guatemala got sick, they told me they would take them to the local public hospital for free (tax supported) care. I was appalled.
We chose to hire an American citizen and my experience disproves George Bush's assertion that no Americans want these jobs. They don't want them at the same rate paid to illegal workers and I don't blame them. We hired an American citizen, paid her a decent wage and paid all the required taxes because that was the right thing to do. George Bush evidently would think I was a fool for doing this. Indeed, at the same time that I paid a legal nanny a good portion of my middle income salary, many extremely wealthy members of the political and professional elite were making news for hiring illegal nannies and refusing to pay the required taxes (remember Zoe Baird and nannygate).
Our nanny’s situation was made worse by the fact that her husband worked in landscaping and his salary was also held down by the competition of many illegal immigrants he worked with. Even on their combined salaries, they barely got by. They could not afford dental care for their son and rarely went to the doctor and, they told me, they were not eligible for any welfare type programs such as food stamps. Here were two citizens working in jobs that George Bush tells us no Americans want. The truth is that American citizens have been forced out of these jobs by low wages. Multiply this story by the millions of illegal immigrants and you see how open borders is destroying the ability of an entire class of Americans to become even marginally self-sufficient.
But that's only what is seen on the surface. The power of comparative advantage (division of labor) unlock once some people are freed up to pursue other, more productive, line of work. In a relatively short amount of time, additional training and skills are acquired by folks who used to do the more menial tasks and their labor becomes an input for more value-adding production. In the mean time, the real effect of what wages can purchase does increase as prices in the lower skilled pursuits lowers, causing costs to decrease to consumers.
Of course we're no longer talking about basic economics here. But what is basic is that basic economic theory teaches one to look at costs both seen and unsee; opportunity costs, economists call it.