People come to this country for a reason. Most illegal immigrants would not be here unless they got something out of it; people hire them and exploit them. Because they are here illegally, they do not seek redress for this (many legal immigrants do not either because they fear authority). Most go without health care until there is a life threatening crisis.
A doctor here set up a system of "free clinics" for anyone who could not afford health care - this includes illegal immigrants - no questions asked. The clinics are run on donations ONLY and are a fantastic resource for the community. I was volunteering at one a number of yrs ago - a woman came in w/ severe 2nd/3rd degree burns on her arms. Seems she was working at a Mexican restaurant and suffered grease burns. She had no benefits, no money - and was fired at the time of the accident. She was suffering horribly and waited days for tx because she was illegal.
I watched this dr. get on the phone, find free meds, tx, and he also reported the restaurant to authorities. (pre HIPAA).
IMO, we should be taking issue w/ the people who hire (and draw/bring) those here illegally, not those coming here to seek a better life. In this country, even the worst conditions are better than what many can afford in their own country. Many put up w/ abuse and the conditions in an attempt to have a better future for their children - they themselves only sacrifice.
I have a friend who is here LEGALLY from India. She comes from money and lived in India w/ servants, many homes and private schools. Yet she choses to live here in a bad area, very small apartment, ride public transportation -- all for the future of her children. The air and water are clean. The education system is good (relatively.) Medical care is available. There are resourses if you need them.
If you have never been to a 3rd world country, or an emerging 3rd world country, you cannot even imagine what everyday circumstances are like. During the adoption of my daughter, I would wake up early - ok, she would wake me up - and I would see dead in the streets...people who just died overnight. Not one or two occasionally, but many, every morning. I would walk down the streets and people would see me w/ a child - and come up and beg me to take their child/children - with tears in their eyes - hoping their children would have a chance, not just at a better life, but LIFE. (At the time I adopted my daughter, infant mortality was 50% by year 5.)
I am only describing the tip of the iceberg as to what I saw...
So, let's not blame the people hoping to improve their lives...
If we want to solve the immigrant problem, look to the employers. IMO, the healthcare problem is being driving by insurance and pharm. companies, for-profit healthcare where gigantic bonuses are given to those that don't even provide health services.