Nobody anywhere precisely "votes for the government they have", pdq, except in some central committee immediately after a revolution (as happened in 1776 in the case of the USA). The people in general didn't vote for that, a small group of radical thinkers and intelligentsia voted for it. They proceeded to fight a war for it, and won that war. After that, the people voted...not exactly for the precise details of how to form the government, but more for the privilege of deciding which members of the intelligentsia would now represent them in the new presidency and congress.

Governments form sort of organically, by a great many processes, very few of which people actually vote for. (People vote for who represents them IN the government.) There are financial factors, trade factors, cultural factors, military factors, and so on. It's very complex. Most it isn't so much a question of the ordinary people voting, but rather of committees of politicians discussing and proposing legislation, and bargaining with each other and with various powerful groups in society. That's how it works.

In the case of our public health care system, I believe it was created shortly after World War II, in response to a society that was becoming more affluent, much larger, and more urban. There was a lot of extra money around, and the government decided that it was now feasible to finance public health care (which it was). What they did has been similarly done in many European countries, and is considered normal there. Those are democratic countries, just as much as the USA is.

Here is a Google link to a wealth of information concerning the Canadian Health Care system:

Canada's Health Care

Interestingly enough, it was the CCF Party in Saskatchewan (one of our western provinces) that started the ball rolling in 1946. That was (and is) a socialist party (renamed since then), and it had been elected by popular vote in Saskatchewan, so evidently it WAS responding to the will of the people in a general sense.

I feel I should explain that "socialism" is not a dirty word in Canada (except to the maybe 20% of the population that would vote Republican if we had the Republican Party here...). Anyway, the CCF started it off, and then the much bigger Liberal Party (which is vaguely like your Democrats, sort of, but not really) picked up the ball and decided it was a timely idea for the whole country.

It remains the single most unassailable instituion in this country. No party promises to eliminate public health care in Canada without cutting its own throat at the polls. And, yes, we are a democracy. Very much so.

The reason Oregonians don't like the idea is simply that they aren't used to it. For the same reason, they don't like wearing kilts or doing the Japanese tea ceremony or being on nude beaches. I doubt that any of these things will change. If I were a socialist, I would not waste my time trying to introduce public health care in Oregon. ;-) What's the use? You can't persuade a cow to dance the polka, even if the cow has the basic physical ability to. The cow doesn't want to. It's suspicious of the whole concept. If cows, however, had the great good fortune to be born in a society where polka-dancing is normal for cows, then they'd just love the idea! ;-)