These views are deeply ingrained in our culture, but cracks are starting to appear with the younger generation, and things may change at some point...maybe. However, when these young people start to hit age 30 or, so, their views start to change a bit and the thought of giving their hard earned $ to people who feel they are entitled to what they work for becomes less palatable, and research, depending on who is doing it, bears this out.
Speaking for myself, I think a single payer system would be a disaster in the US, I lived in Greece from 2001-2003, their single payer system is pretty bad, and last I read it was ranked just above Canada's system (so I will avoid getting sick in Canada at all costs)
Less choice, longer wait times, and worse outcomes would be the result in the US. Even those who get care at free clinics would hate it. Making changes to the affordable Care Act would be our best bet.
I still am in favor of single payer (as I feel it'd be preferable to the system we have now).
However, there would be some "uniquely American" challenges with it, and I think it's a pipe dream if people think it'll go as smoothly as it has in some other places.
One aspect of it (that being the social/cultural aspect as you referenced above) would certainly play a part, as there are a large number of people who are opposed to the government taking it over.
I don't think the US would necessarily have the same issues as Canada did during their early implementation of their healthcare program, as nations that have very low population densities will always have a harder time working out the logistics of how to provide certain centralized services, and keep them reasonably cost efficient.
Especially when it comes to things that are not needed very often, but still absolutely essential/critical when they are needed.
For instance, an MRI machine isn't part of regular routine medical care in most cases, however, it is an essential piece of diagnostic equipment.
In fact, the rough estimate is that 12-15 MRI machines per 1 million people is considered to be enough to fully satisfy medical need.
So as an example, if I were overseeing a region the size of New Hampshire, that had 500,000 people living in it, it would be quite simple. Strategically place 6 or 7 MRI-capable facilities so that anyone who may need to get one can be to a facility in 25 minutes or less (if there were an emergency).
However, that would be a little trickier if dealing with a region that was 3 times that size, but with only half that population. You couldn't strategically place 3 MRI machines in that region because it's not feasible to expect a person to have to be transported 3 hours to reach an MRI machine in an emergency, so you'd have no other alternative but to essentially "over-buy" certain types of medical and diagnostic equipment on a per capita basis in order to be able to provide critical services in the event it was needed. (unless anytime someone needed one, they had to be airlifted to the nearest one, but helicopters aren't exactly cheap either)
Obviously we have certain areas in the country that are sparsely populated where we'd have to over-buy, but not nearly as many as Canada has.
I think the more challenging aspect would be actually getting people to take their own health seriously, because without that, no system is going to be cost-efficient. If there's a significant number of people engaging in behaviors and lifestyle habits that all but guarantee a higher level of healthcare utilization, it's tough to make any healthcare system run well.