The notion that undocumented people don't pay taxes is a total myth. Large numbers of them pay taxes, because you know, they actually care about America and want to contribute. They pay billions of dollars in federal and local taxes and they contribute billions of dollars to social security every year. Yet, they are ineligible to receive the vast majority of government services despite their contributions. Many undocumented people are basically altruistically donating their own money to pay for the services of American citizens. The real entitled people are the ones that think only American citizens should be eligible for services despite the contributions of millions of others to that pool of money.
Why do immigrants care about America? Why don't they pay their taxes to the government in their country of origin? What possesses someone from Mexico to care about American retirees? Not only that, but to care about American retirees more than Mexican retirees? It seems to me more likely that they don't actually care about American retirees. They aren't coming to America to clean toilets and run taco trucks because of altruism. They are coming to America because it benefits them and their families personally. If they pay taxes, it's because it's a sales tax they literally can't avoid paying or if they're using a fake social security number and end up paying social security taxes, it's because they have to in order to work and they don't have a choice in the matter.
Even when they pay sales tax though, and even in the rarer case that they have to pay income tax (although they never usually do), their families still end up using more in services than they contribute in taxes.