Here's a concise statement of part of our problem:
We have both a deep philosophical problem and a practical political problem. The two may be related, but not necessarily. The deep philosophical problem is whether you can walk Western philosophy back from Heidegger and Nietzche and say that reason does permit the establishment of positive values in other words that you can demonstrate the truth of certain ideas.
The practical problem is whether you can generate a set of values that will politically serve the integrating liberal purposes you want. This is complicated because you want those values to be positive and mean something, but you also can't use them as the basis for exclusion of certain groups in society.
It is possible that we could succeed at doing one without the other. For example, the grounds of success of the American political experiment is that it has created a set of "positive" values that served as the basis for national identity but were also accessible to people who were not white and Christian or in some way "blood and soil" related to Anglo-Saxon Protestant founders of the country.
These values are the content of the American Creed belief in individualism, belief in work as a value, belief in the freedom of mobility and popular sovereignty... As kind of a practical solution to the positive value problem, it works pretty well.
And because it has become part of a common culture, defending this basic creed can become a conservative project, in the Oakeshottian sense. We cannot, I think, unthink Heidegger and Nietzsche. But Strauss was far too pessimistic about the West's capacity to sustain itself.