There are many good arguments libertarians put forward against the idea of mandating universal health insurance (either through single payer or a Massachusetts style measure).
It is morally wrong to coerce some people to disproportionately pay for others’ costs or to tell someone who decides to take his chance that he cannot do it.
A mandate would almost surely be accompanied by excessive regulation which would adversely affect medical research and the quality of healthcare provided.
Despite these flaws, it was assumed that such a measure would at least reduce medical costs and thus make life better for a lot of people. However it now appears that even this economic rationale does not hold good.
Of course, the linked article of course only looks only at the Massachusetts model but it seems extremely likely that the same problems will arise in any similar scheme.
So what’s the best solution? I don’t have a completely satisfactory answer; check out, however, Milton Friedman’s short essay on the topic.