Yes, more is being published (and posted) today than at any other time in history, and yes, there are still only 24 hours in each day. So there's no possible way we can read it all. Even if we seriously limit our sights to a well-defined sub-topic of an already circumscribed field, there's almost definitely going to be too much there for us to fully digest. But though more often than not this "information overload" is viewed as a modern phenomenon, exacerbated primarily by the web, it isn't really new. Numerous studies have been published that tell us that even in the relatively early dates of printing people feared that there was Too Much to Know, and as Ann Blair, who wrote that book reminds us:

In the Western tradition, complaints about the abundance of books surface in antiquity (in Ecclesiastes 12:12 or Seneca in the 1st century CE). In 1255 the Dominican Vincent of Beauvais articulated eloquently the key ingredients of the feeling of overload which are still with us today: “the multitude of books, the shortness of time and the slipperiness of memory.”