I can see the reasoning for this. They are tax payers (most of the state budget comes from sales tax and even aside from that, most undocumented immigrants pay income tax) and as long as they are residents, I don't see why they would not qualify. I also know that can certainly stress budgets. Unfortunately our immigration system means that many of these immigrants have no legal path to be here let alone getting citizenship. So I guess if you are against this, bitch to your representative with your dollars to get a non shitty immigration system.
And on the politics of immigration, I've found that most people are in agreement on the process. When you ask people who rant on and on about illegal immigrants what they think the immigration process should be, they largely want a similar process to people who would consider themselves more pro immigration. I recently talked about immigration with a relative recently and mentioned how their was essentially no process when our ancestors came over. She countered by mentioning that my great grandmother went through Ellis Island and eventually had to take a citizenship test. Many conflate immigration with citizenship which is a bit silly. I know several people who immigrated as children and only decided to spend the tens of thousands of dollars to go through citizenship after having lived here for a few decades. Have a conversation with a person who is against illegal immigration and ask how the process should be instead of throwing out talking points. You'll find that many of them actually agree with you.