To what extent is the emerging influence of a new zeitgeist in the 21st century confronting the unquestioned cultural dominance of postmodernism?
There might be a couple of issues that need to be addressed here. The first would be the initial assumption that Postmodern dominance was "unquestioned." I don't see Postmodernism as ever having been unquestioned and seen in terms of cultural dominance. To a great extent, Postmodernism is more of a response than statement. It seeks to critique valences and established norms that seek to impose transcendence upon being in the world. In this, it is a response to a potential statement. I am not sure I have seen it as a statement, something that becomes the transcendent norm. By its own definition, it cannot be. Deconstructionism cannot be a form of construction in the philosophical sense. To this point, I think that the movement has gained traction and is more widely embraced, but to categorize it as "unquestioned cultural dominance" would be something that might need to be "fleshed out" a bit more.
At the same time, I do believe that there might be some elements of an "emerging influence" of a new spirit. What that exactly might be is something to be debated and discoursed, in truly Postmodern fashion. I would say that the rise of groups like Occupy Wall Street and the Tea Party in America and the recent victory by the Socialists in France would help to add to this. There is a new spirit emerging, but I am not sure that it can be fully ascertained in the mode of a "zeitgeist" as of right now. I certainly believe that either way it is seen, it is a response to Postmodernism, the idea that there cannot be a totalizing force. In this, a response is offered to a response, and thus, Postmodernism is still present, yet not as an unquestioned force of cultural dominance. Rather, it is seen as deconstruction sediment upon deconstruction.