In modern times - post-Renaissance - this strain of thought can be traced through the French Revolution, through Marx, to Communism, and still looms like a shadow over the world. In Tom Sowell's terminology, this is the "unconstrained vision": the idea that anything is possible if only human nature can be suitably molded. It is a utopian vision. It promises the moon. And with such incredible promises, equally incredible insults to dignity and humanity have been justified. After all, if one is bringing about utopia, what does it matter (say the utopians) if a few million looters are thrown in the gulag? What does it matter if thousands of opponents are guillotined? One cannot make an omelet without breaking eggs.
By contrast, the "constrained vision" holds that human nature sets certain boundaries which we cannot, as a society, hope to exceed. This view of humanity is that which defined the American experiment. James Madison wrote in Federalist 51:
Ambition must be made to counteract ambition. The interest of the man must be connected with the constitutional rights of the place. It may be a reflection on human nature, that such devices should be necessary to control the abuses of government. But what is government itself, but the greatest of all reflections on human nature? If men were angels, no government would be necessary.
Madison does not imagine, as Plato, that human nature might be molded to produce a class of philosopher-kings. Nor does he imagine, as Marx, that history's inevitable progression through capitalism, then Communism, will result in a New Man capable of exquisite anarchy. Rather, he realizes that men are not and will not be angels, and thus we must deal with them as they are, not as we wish they would be.
And this is where Ayn Rand comes in. A champion of some free-market types, Rand is, unfortunately, no less a utopian than Marx. Her chosen utopia is a bit different in style from most, filled with self-interested, omnicompetent heroes and heroines. In a sense, it is more like Homer than Plato. Galt's Gulch is a modern-day Mount Olympus. But therein lies exactly the flaw: populated by Randian demigods, it is almost literally Heaven on Earth. Rand cannot see how to attain her vision for humanity without creating New Men to her liking. And we've seen where that leads. As Whittaker Chambers writes: "To a gas chamber — go!"
Further reading on this subject: Jason Lee Steorts, Whittaker Chambers.
UPDATE: Also read Richard Reinsch's post on the subject.