I believe you will quickly see some sort of underground system pop up- it usually does in these situations. Something like a black market of health services where people can get care without going through big brother bureaucracy.
You are absolutely correct. There will be Cash system and the insurance system. There will be lower levels of tax compliance and disrespect of the rule or law. Very similar to what you see in Europe. None of which helps stave off the Fiscal crisis facing the country.