The states have always had the same amount of power they have today (for the most part). The thing is, because the President is such a dividing figure, it's encouraging individual states to take paths that agree with their mindset; i.e. more liberal states passing more liberal laws, etc. The thing is, the US mindset (and that of the world) has changed to view the United States as one whole country, much like Germany or China. In actuality, and by the Constitution, it is much more akin to a heavily united Republic.
The thing is, if the US federal government collapsed, the United States and it's culture would not necessarily do the same. Strong states such as New York, California and Texas would most likely be able to carry on individually.