Rand Paul is giving one hell of a speech, and it even exceeds Alexander Hamilton's famously long speech on June 18, 1787 at the Constitutional Convention in Philadelphia, where Hamilton delivered a six-hour speech on what the new government should look like. As Commentary Magazine observed in a review of Ron Chernow's Alexander Hamilton (which I highly recommend),
"It is crucial to recall that, in the six-hour speech at the Federal Convention in which Hamilton outlined his own hopes for the Constitution, he recommended that the President and members of the Senate serve for life, on the condition of good behavior. Indeed, Hamilton was so busy warning the American people against self-flattery that he rarely had a good word for them himself. They were always on the verge of disappointing him and of betraying their own cause. He was not, to say the least, the kind of glibly optimistic democratic politician so popular today."
Rand Paul is most certainly not a "democratic politician." Indeed, earlier in his filibuster, Paul explicitly stated that the United States is not a democracy, but a republic. It is particularly appropriate that Paul is employing the filibuster to achieve his aims, as the measure is by definition, a tool of the minority. And if anything is central to libertarianism, it's that the majority should not be allowed to infringe upon the rights of the minority, nor usurp its private property. This is the core of libertarianism: if government is to exist at all, its function is to protect private property, and little else.