To everyone who is for a tax-funded army and police, but against single-payer healthcare: So you want everyone to be protected from criminals and other countries, got it. What about wild animals attacking citizens? What about Ebola?
If you're for a common defence against those as well, then what's so very different about protecting everyone from cancer?
Sure, without a police or army, the bad results would be more visible, because there'd be headlines like "The evil enemy empire occupying us because we abolished our army has killed 45'000 Americans again this year". But what not having a national service does to a country kills quite a lot of people, too, the number from before, 45'000, is actually exactly as many as have died in the US from lack of health coverage in 2009. Death from lacking health coverage isn't gory, you can't make movies about beating the bad guys, but what you can do is make sure nobody dies from preventable causes anymore.
I think many Libertarians draw an almost arbitrary distinction between the state protecting you from criminals and protecting you from non-human things like cancer. In both cases something is attacking your body, and in both cases without a central organization handling it, not everyone would be protected. Why would we have an obvious good reason to band together to protect us all physically in one case, but in the other "that would be theft and socialism"?