One thing I've seen a lot of people mention is that illegal aliens are "doing the jobs Americans won't do," but this is not true. Most legal residents just won't do those jobs at the artificially low wages. For example, take an illegal resident working 12-14 hours a day in a hot field picking tomatoes during the summer, for maybe $7-8 an hour (which is the actual wage paid to many immigrant workers in the fields in California).
If, theoretically, there were ZERO illegal workers available to do that work, then economics tells us that employers would have to pay whatever prevailing wage to legal residents that the market would support for that labor. So (and I'm making this up since I have no idea what the market would support), let's just say the wages for such labor would go up to $12/hour. At that rate, they are able to find enough resident workers (aka "Americans") to pick all the tomatoes. Correspondingly, the price of tomatoes would go up.
In the end, everything would balance out. People might buy less tomatoes if the price goes up, but eventually the market would stabilize with supply/demand/price. It's not that Americans are unwilling to do those jobs at those wages, it's that employers are (illegally) able to hire workers and pay them less-than-prevailing wages, thereby crowding out legal workers at higher pay. And the workers getting less-than-prevailing wages are unable to afford supporting their families at reasonable levels in many cases, thereby creating a drain on the rest of society (no health insurance, no ability to pay taxes, unable to buy enough food to feed the family, etc.).
Who cares if tomatoes cost more? The other side of that tomatoes-cost-more equation is we end up with more unemployed legal residents (aka "Americans") who become a drain on society, collecting social welfare. This is no different than any other consumer product. Employers hire workers, pay wages, produce a product, and sell the product to cover expenses plus make some kind of profit. Introducing illegal and artificially low wages into the equation upsets the otherwise healthy balance. I have nothing but compassion for a person who comes to America seeking a better life, but in the macro sense, allowing the illegal and unequal pay situation to continue creates a problem for society at large.