The real issue in immigration is the legality of entrants to this country. It is caused not only by the vast economic difference between the United States and its southern neighbours, but also by the unwillingness of the United States government to recognize our own economic need for the low-cost labour illegal immigrants currently provide.
If there are a million, or two million, or ten million illegal Latin American immigrants in this country, it is because there has been, over a course of many years, an artificial and irrational dearth of residency visas issued to persons in Latin America. Just increase the number of visas being issued; in a few years, persons here illegally will find themselves frozen out of the labour market by the arrival of legal immigrants, and they will move on to other places, or back where they came from --- possibly to apply for legal entry.
If we are seriously concerned that the presence of illegal immigrants depressed wages for legal residents, including citizens --- and this is true only at the very lowest economic levels --- raise the minimum legal wage. If that is unpalatable, accept that legal residents' wages will be depressed by the number of immigrants willing to work for the present legal minimum.
At the same time, make it easier for the United States to deport those legal immigrants who are, or become, undesirable: criminals and (I suppose there must be some, though I've never seen evidence of it) lazy people who just want to sit home and watch telenovelas as if they were citizens. Restrict access to certain (expensive) social services: immigrants are not entitled to unemployment insurance; they are not entitled to welfare benefits; they are not entitled to long-term medical care at public expense.
They are, though, entitled to work in safe conditions just like the rest of us, and their children are entitled to be educated at public expense just like our own children. They are entitled to reasonable emergency medical care, and if they are required (like the rest of us) to have health insurance, they are entitled to whatever that health insurance provides.