Let's assume what: 20 million illegals.
Average healthcare costs in the US are $6k per person, so $12B per year. For that savings, you have lots of dead kids lying around and all the little "mistakes" where we found the guy half-beaten to death with his wallet stolen and left him to die because we thought he was an illegal alien.
Also: given that more than half of all bankruptcies in the US are caused by medical bills: how will your idea help? How will it let me get health insurance despite having had cancer?
OTOH, Germany's costs are <$3k per person. So switching to that system, and adding insurance coverage to every man, woman, and child in the US would lower our healthcare costs around $500B per year.