Star Parker, who is apparently black, writes about how universal health care is a slave plantation...of slavery. The crux of this argument, as it is with so many conservative attempts to convince people that they're standing on the Gold Coast of liberal slavery, is that the government may take away one of those decisions you love making, like whether or not you harangue your doctor for a $86 prescription to Flomax or how long to stay at this shitty job given that you think you might have diabetes.
Autonomy in the sense of personal liberty, from a liberal perspective, revolves around the idea that we are free to make decisions about the course and direction of our lives, even though those choices may not be particularly favored by society. The liberal safety net is designed (or supposed to be designed) to allow for people to move from activity to activity, job to job, in order to figure out what works best for them - in essence, to maximize their happiness. There is a concept of shared sacrifice, but there's also a concept of shared benefit - opportunity has costs, and it makes more sense if those costs are distributed so as not to potentially ruin those who seek it. There is still room for success and failure (and the consequences thereof), but you are at least provided the chance to succeed or fail.
Conservative autonomy, on the other hand, is the autonomy of money. It doesn't matter if you're locked into constricting social roles, shut out of jobs, bolted down to a single place doing a single thing for the entirely foreseeable future, so long as nobody tells you how to spend your meager paycheck. If you were going to dinner, liberal autonomy might land you in a vegan restaurant or in a rib shack or at a really terrible taco stand, but the nice thing about it is that you have all of those options. Conservative autonomy would land you at any Applebee's that took your new Discover Card, so long as you didn't get one of those homo arugala salads.
For all the vast and sweeping talk of entrepreneurial spirit that peppers conservative boilerplate, its perception of autonomy is inherently fatal to the concept. You are not bound because you can't leave your job or because you're stuck dealing with a bill for months on end due to a bureaucratic snafu; you're bound because you may soon have the option or requirement to buy cheaper insurance that doesn't disappear once you get a better job offer. You're not bound because large corporations put a depressive effect on wages and seek out effective market monopolies, you're bound because fighting that may result in a package of hot dogs costing thirty cents more. You're not bound because your paycheck hasn't increased in half a decade, you're bound because the person who owns the company may have a three percent increase in their marginal income tax rate for every dollar they earn over $250,000, which will just come out of your paycheck anyway for no apparent reason.
The economic freedom to do exactly what you're told isn't freedom. It's illusory and tyrannical, allowing you the free will to determine which area of your life you're going to neglect and how you're going to neglect it. When you're left entirely to fend for yourself, some will become strong, but most of us will get weaker and thereby forced into certain prescribed modes of behavior. A government that doesn't fight for civil rights necessarily reinforces the inequalities that rule the day.
It's a simple question: would you rather pay the cost of freedom or try to buy it from whoever's selling it? And which one of those two models sounds more like slavery to you?