This problem has always nagged at me. While I'm far from an expert and have taken no relevant classes, old estimates of human arrival in North America of 12,000-14,000 year BP, in my layman's mind, didn't seem to allow for all the human activity that went on in every corner of two vast continents. That included not only establishing populations but wiping out megafauna that withstood the onslaught of many large mammalian predators, from saber-tooth cats to the American lion to the largest and tallest bears that have ever lived (and the wiping out of the predators themselves). This date of 24,000 years BP seems in some ways more reasonable. It's also interesting to speculate how the very first people got here: was the ocean a barrier or a highway? Remember that humans went by boat to Australia some 50,000 years ago.
Traditional theory (NIH/US government illustration)