Until someone else speaks to possibly more up-to-date figures, William H. McNeill, in his work Plagues and Peoples, cites human population estimates of the Americas. Keep in mind this book was originally published in 1976 and a new preface added in 1997. Plagues and Peoples is often noted for being slightly out-of-date. However, I simply haven't come across a more concise work for the subject matter McNeill broaches.

Learned opinion before World War II systematically underestimated Amerindian populations, putting the total somewhere between eight and fourteen million at the time Columbus landed in Hispaniola. Recent estimates, however, based on sampling of tribute lists, missionary reports, and elaborate statistical arguments, have multiplied such earlier estimates tenfold and more, putting Amerindian population on the eve of conquest at about one hundred million, with twenty-five to thirty million of this total assignable to the Mexican and an approximately equal number to the Andean civilizations. Relatively dense populations also apparently existed in the connecting Central American lands.

The high number McNeill is mentioning comes from Henry F. Dobyns' 1966 study that estimates populations in the Americas as high as 112.5 million.

While McNeill doesn't seem to directly cite the lowest estimate, it is possible he is referencing Alfred Kroeber's study that estimated the total population of the pre-Columbian Americas at roughly 8.4 million.