Leo Strauss (1899 - 1973) was a Jewish, German-American political thinker who had a tremendous influence on what remains of serious political philosophy in the United States, and especially on some thinkers who are usually identified as neoconservative. This identification with neoconservatives only occurred after his death, and would probably have surprised him. The pupil who was most faithful to Strauss was Allan Bloom, who never entered politics but instead authored books on Shakespeare and the bestselling The Closing of the American Mind, which popularized Strauss' thought and is quite simply the best book about twentieth century America that I can ever hope to read. I highly recommend it.
There are two basic things you need to know about Strauss and his influence on American politics to be somewhere close to the truth about the man. The first is that Strauss was anti-liberal, by which I do not mean he would have voted Republican but that he had deep reservations about the whole nature of modern, democratic, rights-based politics. This reservation sent him back to a study of classical philosophy. The second thing that it is important to note is that the neoconservatives, whose whole project is based on the export of precisely this rights-based liberal system to the entire world, hence sit incredibly uneasily if they claim the blessing of their former master.
To understand Strauss, we have to understand where he came from. Strauss came of age in Weimer Germany amid the intellectual battles that surrounded the emergence of modern social science and the physical battles between Nazis and Communists in the streets of Berlin. Weimer Germany was the liberal Republic par excellence, in which all manner of crazy political projects and beliefs found succour, which was part in consequence of the dramatic break with the past caused by World War I; one of these political projects was Nazism. Strauss hence saw liberalism at its worst in a weak, directionless polity that eventually allowed itself to be destroyed by Nazism.
The intellectual comitant to this situation was social and political science, which owe their origins to the German thinker Max Weber. The impact of German political thought on America after World War II has been as all-encompassing as it has been ignored, and was driven largely by the emigration of thinkers who fled the Nazis. Social and political science are disciplines that claim to be able to engage in the dispassionate study of social and political problems in the same way that a man can dispassionately study the laws of physics that guide a river. They are fundamentally liberal because they claim that no value is higher than the other; to claim the superiority of a particular value would be "unscientific".
This is the fundamental nature of liberalism: so long as someone desires something that does not violate the law, it is their right to have it. This is what conservatives have long attacked as value relativism. Social and political science became the study of the pursuit of social and political desires, without allowing itself to comment on what these goals should actually be. This means the goal might, for instance, be Nazism.
Weber's ideas roosted on the East Coast and in Chicago and soon became American orthodoxy. Strauss also came to America and he recognized these phenomenon from the old country, and he remained as unconvinced when the fundamentals were dressed in American garb as he had been when they wore lederhosen. Strauss thought that liberalism led to nihilism because if nothing was valued higher than anything else, then nothing had value. Furthermore, liberalism was a "seminary of intolerance" as he says in his book Natural Right and History, because the consistent liberal can have no objection to the Nazi without recourse to something outside of liberalism; all values are relative, after all, and a system that is based on what men desire cannot stop a man desiring to be a Nazi. The system might be saved if all other men have banded together and passed a law that outlaws Nazism, but this law is also based only on people's desires and can be repealed if they all decide to be Nazis. Without a higher metaphysical standard, liberalism hence contains the seeds of its own destruction.
Strauss hence argued that liberalism could never be separated from some other metaphysical belief. Something like the Ten Commandments or a theory of natural law had to, in the last analysis, provide the fundamental basis of inviolable rights. This is the basis of Strauss' interest in the noble lie, a concept derived from Plato which states that some sort of irrational belief has to lay at the foundation of a political system to hold it together - such as, for instance, the belief in a God who prohibits Nazism. This concept was vulgarized and taken to mean that his supposed followers were encouraged to lie about Iraq's weapons of mass destruction to justify the invasion, but this is entirely removed from Strauss' point that fundamental rights have to be justified by an irrational belief.
The neoconservatives were certainly heavily influenced by Strauss, but to claim that they are "Straussian" or that his ideas lay at the heart of their policy is highly misleading. Strauss was highly pessimistic about cultural conditions in contemporary America, believing them to be a reflection of the relativistic nihilism that he so scorned. He urged a return to the study of clasical philosophy and of classic notions of virtue, arguing for the existence of duties as well as rights. He did not think that the fundamental tension between excellence and equality was resolvable, and his opposition to liberalism did not lead him to a simple-minded acceptance of some tyrannical alternative. His criticism of liberalism was as a friend, not a determined enemy. He kept thinking, and kept writing, precisely because the problem of how humans should live together in society could not be solved.
The neoconservatives, on the other hand, believed this question to be resolved: the fundamental problem of human living-together had been solved, and the solution was the United States of America. Francis Fukuyama, who was a student of Allan Bloom, stated this worldview most concretely in his The End of History, in which he claimed that the question of what the best type of regime was had been solved by the United States. Entirely missing from this analysis is Strauss' pessimism about American liberalism, which could hardly have made him sanguine about its export all over the world. Furthermore, his profound understanding of political problems and their inherent unsolvability would have made him highly sceptical of the idea that a new regime could be easily enforced by the barrel of a gun. I suspect he rolls over in his grave whenever he is associated with it.