This fascinated me, so much so that two days later I'm still thinking about it. It's a Reagan quote, which makes me think that this is supposed to be some kind of conservative ideal or something to show that conservatives are right. Here's the thing, though: I suspect most liberals would agree with Reagan's idea here, perhaps with just a small tweak.
All things being equal, I'm hard-pressed to imagine anyone who would want the government to run her life. It's big, it's blundering, and it's generally not very forgiving. Republicans are famous for this, and while American conservatism today usually doesn't live up to that ideal very well, the idea that Republicans want the government as small and unobtrusive as possible. The way I walways thought about it, Republicans want government to get out of the way as much as possible. Depending on the Republican, they might make exceptions for the national defense or the definition of marriage, but that's the basic idea.
Here's the thing, though: in my experience Democrats also don't want government to interfere more than it needs to. The difference is that Democrats think companies and non-profits and simply an unequal distribution of resources are just as much a danger that needs fighting as anything al-Qaeda has pulled off. If we'd worked out a way to give everyone the money necessary to meet their basic needs (food, shelter, healthcare, education, etc.) I'd be more than willing to shrink the government down so all it did was keep the borders secure and make sure the interstate highways were in working order, and maybe a few other extremely basic things like that. I'm actually not a fan of big government.
But Utopia's just a small town upstate, not any good description of how things actually work. Companies exist to make a profit, not help people or even treat them fairly. People have their own biases and will put their own family and friends' comfort over the basic needs of a complete stranger. And everyone comes with their own biases and ideologies, and will tend to act in a way that lives out those ideologies. This is just human nature and I don't know that it's particularly immoral that people act this way. (Not particularly saintly, either, but certainly not heinous.)
In light of this, I think a lot of the things Republicans consider "interfering" is protecting. Let's take one example: the insurance mandate and the blow-up over whether religious groups needed to pay for insurance covering procedures that went against the group's beliefs. I believe access to health care is a right, perhaps not legally but definitely philosophically. I also believe that each individual (not her employer) ought to be the one deciding which medical procedures she'll actually have. The medical system is expensive but also complicated, and so I don't think it's reasonable to ask any individual to navigate it on her own; it needs systemic reform, and it needs to be providing universal access. Both of those are big enough problems that you need a group action, organizing and implementing a system that makes at least basic health care affordable for every one. And this implementation needs to respect individual dignity and autonomy. That means that if I'm poor and I'm sick, I shouldn't have to rely on some charity that might have special requirements. I also shouldn't have to face special requirements to access government care that middle- or upper-class people don't face. (I'm thinking of people on Medicare who have to prove they were raped in order to get an abortion, or where the government says they can't buy certain kinds of food, or requires them to pass a drug test before they get tax dollars.
This all falls under the rubric of protecting people. The threat here isn't a terrorist cell but a company or individual or church or other institution imposing its ideology on other people. As I said, I can't imagine anything more natural in the world than a church using its resources to advance its agenda. Ditto for a company or civic group or even a wealthy individual. The way the government protects us, and in particular "the least of these," is by putting limits on what those groups can actually do.
This meme clarified for me a basic difference between conservatives and liberals. Conservatives seem to think the best way to get at liberty is by leaving people to their own devices. Liberals, I think, see threats other than national security threats that people need protecting from (or at least an organized, collective way to protect themselves), and they recognize that the best road to liberty often involves laying down some ground rules establishing just how much of public resources any one individual can claim. If society was equal enough that no one could take away what his neighbor truly needed, I'd be all for shrinking government down to the size of a breadbox. But, reality being what it is, I don't see that happening any time soon.