At http://archaeologynewsnetwork.blogspot.co.uk/2014/01/what-killed-great-b… … one of the most implausable theories is that humans were capable of killing off the great herds of the Ice Age – such as mastodon, mammoth, giant bison etc. Armed with bows and arrows, they are supposed to have gone on a killing frenzy and set about other animals too, such as giant beaver, giant sloths, and the like, as well as the herbivores. I've always supposed the overkill hypothesis was proposed because its proponents did not want to face up to the inadequacies of uniformitarian change. Instead of admitting something extraordinary had happened, on more than one occasion, they invented the idea that humanity was the agent of catastrophic change.
In this link news of a paper that is also disbelieving of the concept of overkill. They studied the remains of animals in the NE of N America – including New York State, and they found Ice Age mammals were decimated on more than one occasion (which was already known) and most of them had disappeared by the Younger Dryas event (when they finally died out, also well enough explored in other studies). In other words, the main extinction event occurred long before humans entered N America.