The USA feels all people should have healthcare; young, old, immigrants, rich, poor. So make everyone pay incrementally. Support NATIONAL healthcare with NATIONAL SALES TAX on everything purchased; food, web purchases, everything. Every will pay; employers, consumers, rich, and poor, immigrants, everyone.
I don't know how to craft a good infrastructure for national health care, but we currently have a good base to build on. As long as you have money to support a program, you don't have to worry about cost-cutting on services.