Apparently the other camelids (such as llamas and alpacas) also originated in North America and only later spread to South America.
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CAMELS. In 1836 Maj. George H. Crosman urged the United States War Department to use camels in Indian campaigns in Florida because of the animals’ ability to keep on the move with a minimum of food and water.
http://www.tshaonline.org/handbook/online/articles/quc01