I'm Brazilian. Brazil have a free healthcare system called "Sistema Único de Saúde" ("Unified Health System") or, as we often call it by its acronym, "SUS".

While I personally had a fair good experience with it when I needed medical care, SUS is not perfect. There are notorious disparities between Brazilian states regarding to how many public health financing from taxes each city any state gets. For example: the state of São Paulo has better public healthcare than, say, Minas Gerais (and I'm talking about two states that I personally know and resided in, so I'm not talking about something I read somewhere or something I heard from someone). Even when they're neighbors. It's not because Minas Gerais is worse than São Paulo, because it isn't, it's because São Paulo gets to get more tax funding.

The following is recent news (as from this week) from a major Brazilian news television program, translated to English:

That man is hospitalized through the Brazilian public healthcare system. Cases like his happen on a daily basis throughout the Brazilian territory, especially in the northern states, but not limited to. It's just that his case got to get the attention of the media. Several Maurílios (and Marílias) face similar bureaucratic slippery slopes every day.

Is the private healthcare better, then? Hell no, of course not! Our "convênios médicos" are as bureaucratic as the US healthcare insurance, perhaps even worse. The only thing that's far from bureaucratic is "particular healthcare" because the patient pay directly to the doctor, but it's generally expensive and far from the reaches of the reality of millions of Brazilians, and they don't really cover all the medical needs (e.g.: paying directly to a doctor won't cover the need of MRI scanning, because individual doctors often have no MRI machines for their own medical service).

The "Sistema Único de Saúde" is something to be improved and it's far from perfect and it needs lots of fixes, but it's undeniably a public healthcare system model to inspire Americans so they can begin with a proper healthcare system nationwide. I don't really know British NHS or Canadian public healthcare systems, but Brazilian system is probably unique because of how many people it serves (216 million people, more than UK and Canada populations summed up).