It is hard to say with any certainty, but we can make some educated guesses based on domestications elsewhere.
For example, considering that horses, camels, pigs, and oxen were domesticated elsewhere, and relatives of camels were domesticated in the Americas, if these hadn't gone extinct in the Americas they very well could have been domesticated. Many surviving peccaries and llamas have been domesticated, so extinct forms could have been as well. We have domesticated a lot of both land and water fowl, including some in the Americas, so extinct forms could have been domesticated in the Americas as well.
On the other hand, bears and big cats haven't been domesticated anywhere, so it is unlikely they (or other animals filling similar niches like Nimravidae) would have been domesticated in the Americas. Although it would be plausible for the dire wolf to be domesticated, humans would have brought their own dogs so this wouldn't likely have happened, and non-social canines probably wouldn't have been domesticated.
There are other animals where the situation is less clear. Glyptodonts, Notoungulata, and ground sloths were pretty diverse, so perhaps there were some varieties that could have been domesticatable (although I am not sure why someone would want to domesticate a Glyptodont). Reindeer have been domesticated, so perhaps some of deer varieties could have been depending on their behavior. Similarly, Asian elephants have been tamed (but not domesticated due to their long reproductive cycle) while African elephants haven't based largely on different temperaments, so it is possible some of the smaller varieties of elephant relatives might have been had short enough reproductive cycles and good enough temperament to be domesticated. As mentioned previously, most varieties of llama and camel have been domesticated, so the superficially similar Litopterna might also have been.
It is much harder to say with terror birds, humans never really had any contact with large carnivorous terrestrial birds. If they imprint like many bird species do then domestication would have been easy, otherwise it would probably have been extremely difficult.
Similarly there really are no living enormous rodents, so it is hard to say what we would do with something like the giant beaver. Although we have domesticated the largest living rodent, the capybara, it is naturally a herd animal, so it isn't a good basis for comparison. It is a South American animal, though, and it has extinct relatives that could have been domesticated as well.
Edit: I originally incorrectly said Asian elephants have been domesticated. They have only been tamed.