http://www.wsj.com/articles/illegal-immigrants-get-public-health-care-despite-federal-policy-1458850082
http://www.latimes.com/local/political/la-me-pc-california-senate-approves-health-coverage-for-some-immigrants-here-illegally-20150602-story.html
There are a lot more but since you have more time than I do research it yourself.
your first link is just headline and I can't read the entire article since I don't have a membership to WSJ online. I assume you've read the entire article and not just the headline so please fill in the details for us.
The 2nd link is about SB 4 in CA which allows ~ 170k children of immigrants to have access to some basic healthcare but it's not something created for illegal immigrants (and it doesn't appear to be completely free in all cases).
The only requirement is income and NOT immigration status. In other words it's available to children of low income citizens as well so not at all what Stein was alluding to in that quote (assuming that quote is even real) which says that access is due to inability to prove legal status.
He makes no mention of income requirement or the fact that this program is also (and originally) available to poor citizens and their children. So this can't be what Stein was referring to. It appears the original version of the bill was going to allow a limited number of illegal immigrant to PURCHASE insurance on the CA exchanges (since Obama care restricts this) but that was taken out and the bill that was signed only offers access to Medi-Cal to children below the age of 18, again available for all and based solely on income level of the parent and not immigration status.
The arguments for including these children are both financial and humanitarian. First the financial argument is that it costs the state more for these kids to show up in an emergency room than to give them access to some basic healthcare/preventative medicine
The humanitarian argument is that the children are not responsible for the "sins" of the parent and as a humane (and you might even argue Christian) society we provide some level of care for the poor (on in this case children of the poor) Of course there is a pro-life aspect to it as well as an aspect of helping the poor.
I don't subscribe to a religion that suggests I should help the poor and of course I'm all for abortion so I'm fine if these kids die from lack of access to healthcare. I just consider it to be a very late term abortion I assume you're all for this type of abortion as well
It's hard for me to argue against the financial aspect though. I'd always rather pay less than more. I assume even you agree with that