I specifically mentioned the Luddite Fallacy with respect to the expressed concerns about healthcare. The notion that the cost to provide healthcare will not change relative to the ability of people to pay for healthcare is a fallacy of not understanding that technology can and does improve, become more efficient, and come down in price. This is, in a sense, the modern form of the Luddite Fallacy (since we've mostly gotten over the fear of having our jobs replaced by machines...the machines have already won).
I think this attitude of "healthcare is expensive, deal" is particularly dangerous because of how insidiously defeatist it is. You start thinking nothing can ever improve healthcare, so why bother paying for research into improving healthcare, so healthcare doesn't improve. Universal healthcare is socialist and evil and doesn't work, and nobody ever solved problems by increasing the size of the public sector and funding research through the public sector...
To which I say: BULLSHIT! This is the very fundamental problem that we face. The private sector has no reason to decrease the cost of healthcare when they can just pump up their profits instead. Or, at least, they'll have no incentive to do so until healthcare is rationed. Or they'll start to have an incentive to be cheaper when people can no longer afford insurance. Either of those scenarios is not pretty, and will have a nasty transition period where people cannot get the care they need while the private sector figures out how to do things cheaper.
The public funds fire departments because structures burning, even private homes, is bad for society. If your house burns you become a burden on your neighbors or on the community, you can't be productive in the economy, etc. Why is it so hard, then, to see the parallels with healthcare? Healthy people are as or more beneficial to society as people with homes! If we can protect people's homes, why can't we protect their health?!?