It is YOUR responsibility, NOT the governments!
A government's responsibility is good governance. This is usually achieved by formulating and implementing policies that lessen social and economic disparities, create opportunities, empower the individual and provide the basis for social and economic opportunity and justice. Such policies represent an investment in the biggest resource any country has; its people. This means getting real bang for your tax bucks.
How can anyone be responsible for their own health care when the private health insurance sector has proven itself irresponsible and the ability of assuming this responsibility is beyond the financial capacity of tens of millions of American citizens?
If you don't want good governance (but you will still have to pay taxes), you can move to any country south or your border. Or try the Philippines, China, Afghanistan, Uganda, Zimbabwe, Sudan et al; there are hundreds of countries where the prevailing attitude is 'every man, woman and child' for themselves. There you can bribe your way to good health care outcomes, regular mail deliveries, garbage collection, employment, a roof over your head, you name it, there is an appropriate bribe for every mood and occasion.
My business partner's mother contracted Leptospirosis during sever flooding in Manila last year. She was in a private hospital for three months, due to complications, at a cost of US$1000 a day. There was no insurance or government assistance to pay for it. The family paid for everything out of their own pockets, including the ongoing full-time care she now requires at home. Is that the kind of system that you want America to emulate?
Perhaps you are financially independent enough that paying $10,000 or more for health insurance every year doesn't bother you. Or, perhaps, you can afford to pay for all of your treatments with your Platinum Amex card. Good luck to you if that is the case, but that doesn't help anyone else.