I am not sure that most people would agree with you on that; at least, I personally do not agree that people who are in this country illegally do not deserve taxpayer funds. I think that's very similar to saying that someone who pays no taxes does not deserve taxpayer funds, which I also disagree with. Since most people who are living in this country illegally are paying one form of tax or another, the only difference between the two groups is the amount they've paid.
Receiving taxpayer funded benefits such as K-12 education or health benefits has nothing to do with whether someone pays taxes or not when (think retired or disabled people for example) but rather whether they are living in the country legally or not.