I see. So, Christ was not addressing the individuals responsibility to other individuals, but rather was saying what secular nations should do, and should do with the taxpayers money. Therefore, he was criticizing Rome, and how the Romans government did not spend it's taxpayer money on aliens who were incapable of supporting themselves. Interesting.
You quote the Torah, which, as you may know, was the rule of law for the nation of Israel, a theocracy.
The United states is not a theocracy, it is a secular Republic, and in a secular nation taxpayer money is not spent based upon religious doctrines.
I suggest you read Romans 13. Paul makes an absolutely clear clear case that Christians are to obey the civil law. Certainly I have an obligation to aid any individual I come across who needs help.
however, I am also obligated to follow the law. ALL people are obligated to follow the law. Illegal aliens have broken the law, legally, they have no business being in this country. They legally have no right to taxpayer funded programs or benefits, designed for American citizens, legal immigrants do.
The law also specifies the criteria for granting residency based upon political or religious harassment or danger. Wanting more money is not a criteria that is acceptable.
Christ always speaks in terms of a followers individual responsibility to other individuals or groups. He does not address government obligations. He never condemned Rome for any of it's political positions or actions.