First, I think we should all agree that single-payer health insurance is probably the most un-conservative idea that one could possibly imagine and that this is one issue that Republicans should go to the mat and beyond fighting against.
But what I most object to is the philosophy behind single-payer health insurance. It is a philosophy of dependency on government. It is the philosophy of entitlement - that we are all entitled to certain things without having to work for them. It is the philosophy that government should provide citizens with needs, even if they are able to pay for them themselves. It truly is the old-school hard-core central-planning-style socialism.
De Tocqueville was an amazing man. In his book Democracy in America, he wrote (among many other things) about ways that a democratic nation like America might succumb to despotism. It would of course be different than the despotism of a king, emperor or tyrant since a democratic nation has none of these. Instead, he wrote (yes it's long but read the whole thing anyway):
"I think, then, that the species of oppression by which democratic nations are menaced is unlike anything that ever before existed in the world; our contemporaries will find no prototype of it in their memories. I seek in vain for an expression that will accurately convey the whole of the idea I have formed of it; the old words despotism and tyranny are inappropriate: the thing itself is new, and since I cannot name, I must attempt to define it.
"I seek to trace the novel features under which despotism may appear in the world. The first thing that strikes the observation is an innumerable multitude of men, all equal and alike, incessantly endeavoring to procure the petty and paltry pleasures with which they glut their lives. Each of them, living apart, is as a stranger to the fate of all the rest; his children and his private friends constitute to him the whole of mankind. As for the rest of his fellow citizens, he is close to them, but he does not see them; he touches them, but he does not feel them; he exists only in himself and for himself alone; and if his kindred still remain to him, he may be said at any rate to have lost his country.
"Above this race of men stands an immense and tutelary power, which takes upon itself alone to secure their gratifications and to watch over their fate. That power is absolute, minute, regular, provident, and mild. It would be like the authority of a parent if, like that authority, its object was to prepare men for manhood; but it seeks, on the contrary, to keep them in perpetual childhood: it is well content that the people should rejoice, provided they think of nothing but rejoicing. For their happiness such a government willingly labors, but it chooses to be the sole agent and the only arbiter of that happiness; it provides for their security, foresees and supplies their necessities, facilitates their pleasures, manages their principal concerns, directs their industry, regulates the descent of property, and subdivides their inheritances: what remains, but to spare them all the care of thinking and all the trouble of living?
"Thus it every day renders the exercise of the free agency of man less useful and less frequent; it circumscribes the will within a narrower range and gradually robs a man of all the uses of himself. The principle of equality has prepared men for these things;it has predisposed men to endure them and often to look on them as benefits.
"After having thus successively taken each member of the community in its powerful grasp and fashioned him at will, the supreme power then extends its arm over the whole community. It covers the surface of society with a network of small complicated rules, minute and uniform, through which the most original minds and the most energetic characters cannot penetrate, to rise above the crowd. The will of man is not shattered, but softened, bent, and guided; men are seldom forced by it to act, but they are constantly restrained from acting. Such a power does not destroy, but it prevents existence; it does not tyrannize, but it compresses, enervates, extinguishes, and stupefies a people, till each nation is reduced to nothing better than a flock of timid and industrious animals, of which the government is the shepherd."
The reason why De Tocqueville couldn't come up with a name for this despotism was because it hadn't yet been invented in the early 19th century. He was writing of the despotism of the welfare state. It doesn't crush a person's spirit like a jailhouse tormentor might, but it simply attempts to divert a person's life into a prescribed direction, like a shepherd does for his flock. I don't want government as my sheperd. And that is why I oppose single-payer, and that is why I am a conservative.
P.S. For those of you seeking conservative ideas about health care, see this website and associated book from the Cato Institute.