I believe that the media, TV, Internet etc. feels the need to attract people's attention with dramatic, over the top interpretations of pieces of data. So a story on an interesting Mayan calendar becomes the end of all times, it is alarmist and not necessary but it is what sells ad space, clicks on a link and drives our consumerist society.
American TV is obsessed with all sorts of things that are fantastical, but this is just representative of what our culture thinks is entertaining these days. We all sort of sense that our culture is decaying and we sort of like the stories about how we triumph in the end. Truth be told, we probably would not triumph but that doesn't make a good story. These programs are like another drug that we can use to de-sensitive ourselves from reality.
American TV is obsessed with post-apocalyptic stories, and this is symptomatic of our culture's obsession with disaster and apocalypse that we see in the news and on fictional TV shows. We are also obsessed with shows about mystical monster creatures (like werewolves and vampires) and shows about horror and gore (American Horror Story) and serial killers (Dexter).
Television is a reflection of pop culture. As such, the claim that American TV is obsessed with this particular aspect of pop culture is rendered false by design. The real question is why is American pop culture obsessed with this genre? Why post-apocalyptic instead of just apocalyptic? Why America instead of the world? It seems that the obsession is most frequently expressed in the country which is in constant pursuit of new technology, but, unlike other countries equally, if not more advanced, the state of human connection and the challenges technology has been presenting to that reality of connection are only beginning to significantly complicate our idea of humanity. It could be / has been argued that we are equally obsessed with the super natural realm as well, but, historically, obsessions with vampires and the like have been reflected desires of immortality and fear of death. Is it still? Or is it being designed as yet another reflection of humanity? What it means to connect, to be human? Our post-apocalyptic scenarios range from moments after the cataclysmic event to decades or even centuries later, yet they have a commonality to them. The control, distribution, or removal of technology. If technology is a tool and tools shape our society and society shapes the individual, are we really okay with what we are becoming? Is it forcing us to question what humanity is? Are we fantasizing about a forced reconnection?
Post-apocalyptic stories provide a way for us to explore many different facets of humanity so no, American TV is not too obsessed with it. It is, however, willing to settle for a poor quality of show. While these stories may be popular right now, they have always existed and will continue to always be around.