1891
I'm not sure I wouldn't just let the damn thing collapse and then get rid of it with something new.
The problem is what's the new thing going to look like? Insurers make their money by insuring healthy people, and they need healthy people to pay for the sick ones. They loose money by insuring sick people, since the sick people will never pay the insurance company more than they spend on their illness (if sick people paid the insurance company more than it cost to treat themselves what need would they have for an insurance company?).
So in order to get insurers to cover sick people, you need more healthy ones to sign up. Hence the mandate. And you need to insure poor people, or they wind up costing even more on the dole. Hence subsidies. In order to cover sick and poor people whatever gets put in place is going to wind up looking a whole lot like Obamacare, which itself was based on the plan Mitt Romney used in Massachusetts.
Now if you want scrap either insuring the poor or insuring sick people (or both) it gets a lot easier. Indeed, the current reverse Robin Hood plan of the GOPs is sufficient. But at that point I think you're going to have a lot of pissed off people, as the GOP is finding out much to their chagrin. Like I said, the Djin is out of the bottle.