In North America, camels and horses went extinct long before anyone had a pressing need to domesticate similar species. The American species went extinct between 13,000 and 10,000 years ago. North American camels were extinct for at least 4000 (may be closer to 6000) years before their Eurasian counterparts started being domesticated. Similarly the last horses in the Americas were extinct some 5000 years before horses in Eurasia were domesticated.

Also, to clarify something, the people living in the Americas at the time of these extinctions wouldn't be the "first" Native Americans. Those living at the time of the extinctions circa 10,000 years ago, would be at least 6000 years removed from the first people to reach the Americas, probably closer to 8500 years, possibly as much as 15000. Those numbers are based on the earliest confirmed evidence for humans in the Americas, the earliest plausible evidence, and the time at which genetic evidence indicates that the ancestors of modern Native Americans became a distinct population isolated from Eurasians, respectively.

Even if these horses and camels had survived into the present, they are different species from their Eurasian counterparts. We don't know about their temperaments and whether they would have been a help or a hindrance to domestication. We also don't know if people would have been motivated to domesticate them. We're still working out why anyone domesticates anything. Sure, it make sense to us in hindsight, but at the moment is it really a significantly better option than hunting?