In Britain 80% of the people rely solely on the National Health System. The elite 20% have private insurance and use an elite private health system without lines, with nicer rooms, and better service. That is a two tier system.
We have a two tier system in the U.S.. The difference is that in the U.S., the middle class is part of the top tier.
The danger for the middle class:
The top 20% are confident that under a public health system they will still have access to elite health care. They are probably eager for a system where they mingle less with the middle class. So, that's 20% that aren't afraid.
The bottom 20% figure they will be no worse off than they are now with the mishmash of health providers they have access to and it may be better because there will be more political interest in the facilities and procedures they use. So, 40% of the country is okay with and perhaps eager to move to something more like a British system.
The 60% who will drop down a level better keep fighting and not be fooled by soothing rhetoric. Otherwise, they will find out what kind of health care the elite think is adequate for the lesser classes.