Considering that Australia was settled upwards of 50K years ago by the aborigines, it's not too much of a stretch to consider that they also managed to make it here. The Americas were also likely visited by people from Asia and Europe across the northern ice flows.
Why did the Asians come to dominate? I was reading at one point that the Asians had a crucial innovation: the domestication of the dog. This gave them a big advantage versus some of the big nocturnal predators that inhabited the Americas at the time (an early warning at 3am that a sabertooth is around would make a big difference in your survival prospects)
"Before 135,000 years ago Neanderthals had domesticated dogs. 100,000 years ago they also had sheep, goat, cattle, pig and possibly reindeer. It's very possible that these special relations with animals evolved through the use of signals and simple instruments used for communication during their hunting activities . These animals weren't domestic in our sense of the word, rather they roamed around freely, and could be called upon. This same method was used in many parts of Scandinavia. Dogs probably played a key role in both hunting, driving animals and for defense and protection. They also knew the properties of various plants. Stimulants were used to tamper with activity level."
From this excellent article: The Neanderthal Theory
Makes sense. I suppose they wouldn't have had to come from Australia to America, perhaps they came from elsewhere? Or does the timing preclude it?