The libertarian ideal is that the individual should have the maximum amount of freedom, tempered only by an absolutely minimal amount of interference from government. Some libertarians go so far as to favor the abolition of the state entirely, while others believe that the only legitimate governmental institution is a minimalist judiciary to arbitrate disputes between citizens. Libertarians generally feel that the state has no business regulating the activities of citizens and that everything should be left to the free market.
In some ways, Thomas Jefferson leaned towards libertarianism. Intellectually, at least, he favored a minimalist state that interfered in the lives of its citizens as little as possible. As President, he shrank the government. In his struggles with Alexander Hamilton, Jefferson was the champion of local control against those who sought to increase and expand the power of the central government.
So, it is clear that there was a streak of libertarianism that ran through Jefferson's political philosophy. The same is true of 21st Century Jeffersonianism. We believe with the libertarians that the telos, the end towards which we strive, should be for every individual to have the greatest amount of freedom possible. To this end, we believe in a small government that intervenes in the personal lives of the people as little as possible.
But Jefferson, despite efforts by libertarians to claim him as one of their own, would never have gone nearly so far as modern libertarians do. Jefferson understood that, in addition to being a large number of individuals, society is also a collective whole that possessed collective interests, and that government is sometimes the only means to further those collective interests. As a state legislator in Virginia, Jefferson authored laws to regulate those activities of citizens which he thought needed regulation (smallpox inoculations, for example), and while he was certainly a small-government oresident, he would have seen any suggestion that the government be abolished as ludicrous.
The problem with today's libertarians is that they are, by and large, devotees of pure theory, rather than practical men and women who are willing to adjust their beliefs to the realities of the modern world. Some of them are indistinguishable from the most rabid religious fundamentalists, holding up the collected works of Ayn Rand as their Bible. And one of the lessons of history is that when devotees of pure theory are actually handed the reins of power, the results are usually disastrous. One can look at the French Revolution, the Russian Revolution, and the economic meltdowns that have resulted in innumerable countries from religiously-strict adherence to either socialist or capitalist economic philosophies.
If you want a real-world example of what happens to a society without a government, take a look at Somalia.
And then there's the fact that strict adherence to libertarian ideas of individual freedom result in the exploitation of individuals. Consider the case of Michael Clauer of Frisco, Texas. While serving as a National Guard officer in Iraq, bravely fighting for his country, his paid-for home back in Texas was foreclosed on and sold because his wife had accidentally missed a few payments to their local home owners association. She had been suffering from depression due to her husband's absence and had allowed the mail to pile up.
In the libertarian world, this is all a matter of property rights and the sanctity of contracts, and therefore it is quite fitting and proper for Clauer and his family to be kicked out of their home. But the conscience of every decent human being finds this revolting and, more to the point, feels that the rights of the Clauer family have been grossly violated. Surely, one of the roles of government is to protect citizens from being victimized by such exploitation.
Jefferson was, above all else, a man of the Enlightenment, who believed that human reason was the ultimate guide. This freed him from blind adherence to strict ideologies and gave him the ability to adjust his beliefs as to the best courses of action in light of actual circumstances. In this, 21st Century Jeffersonians follow their namesake. While libertarianism has many useful ideas that should be warmly embraced, following its theories to their ultimate conclusions would simply drive us off a cliff. For that matter, the same is true for modern liberalism and modern conservatism.