Keith - yep, bison, moose, grizzlies survived but the Americas lost over thirty genera of large mammals (elephants, rhinos, giant ground sloths, armadillos the size of a VW, bigger buffalo, a bunch of large predators, including sabertooths, a very large bear and lions) within a few thousand years after humans arrived. We had a large mammal diversity comparable to Africa until that time. Same thing happened in Australia and New Guinea, including huge lizards and snakes. We wiped a lot of very large birds (e.g. moas in New Zealand, dodos on Mauritius), and large tortoises on many islands, as soon as we arrived. The process was slower in Eurasia, presumably because it took a long time for the human population to increase and the animals had some time to evolve behavioral responses. The story has been the same all over the world - when humans arrived, first the big stuff went, then a lot of smaller stuff especially on islands, due to things liked deforestation. Haiti and other Caribbean islands are prime examples.
It's all very interesting, and very open to debate and speculation. The arrival of humans in North America was very thin and spotty for many thousands of years before their population density, and the efficiency of their weapons, could conceivably account for many of these extinctions during the late Pleistocene and Holocene. Humans are indeed very efficient and relentless predators, but there was also advances and retreats of glaciation, the Quaternary extinction event, massive wildfires due to rapid climate change (which had nothing to do with scant human activity), worldwide volcanic activity, and even possible cosmic events like meteor impacts. The mere presence of charred bones in ancient fire pits could indicate hunting, or scavenging of animals that died from other causes, or more likely, both.
But having seen how quickly hunters legally made a healthy population of wild ringneck pheasants nearly extinct in my state after the killing of hens was permitted, I would never argue that man couldn't wipe out a species. Sad that our game commission could never acknowledge and rectify that error.