Believe it or not, I actually don't have much of a problem with illegal immigration itself. In a way, it's flattering that so many millions of people are desperate enough to enter our country that they are willing to put themselves in great harm's way in order to do so. Some of the anecdotal stories involving the horrific arrangements people make with "coyotes," guides who bring them across in exchange for promises of future earnings, leave no doubt as to the degree of motivation illegal immigrants have to enter the United States.
Similarly, I can agree that once here, most of them seek only to make money and create a better life for themselves. They do so often through manual-labor jobs that tend not to appeal to American citizens. Although their presence creates a bit of an underclass in society, they do mitigate some of the strain that minimum wage places on the labor supply. So...that's good, because the minimum wage is a destructive policy that only hurts the workforce. In a way, illegal immigrants fill a vital need within our economy.
However, the problem arises when these people have entered this country illegally, yet avail themselves of services paid for by taxes and reserved for US citizens. Hospitals, schools and the like are forced to accept people with no legal right in the country, and expend resources that are reserved for people who bothered to go through the process in the first place. Quite simply, those are ours. As compassionate as it is to be welcoming to all people, we have a spending problem in this country, and you don't lend your hose to your neighbor when your own house is on fire.
I'm not indifferent to the fact that illegal immigrants are people, though, and as such, they will get injured or sick in this country, and they will have children who need education. That said, I see no reason not to require upfront cash payment for services from people who cannot produce proof of citizenship, either. I don't have a problem with them using the hospitals and schools...but they don't get the benefits that citizens do. Make our services available for a fee, demand payment in cash upfront, or a guarantee from their country's embassy or consulate, and we have no problems.