The scholarly consensus of the estimates of the native indigenous populations of North America have been trending upward over the years and it's based on sound archaeological evidence. You might find the following informative.
The Native Population of the Americas in 1492
Second Revised Edition
Edited by William M. Denevan
With a Foreword by W. George Lovell
How many people inhabited the New World when Columbus landed on Hispaniola in 1492? How did the arrival of Europeans spark the population decline of aboriginal people in the New World?
William M. Denevan writes that, "The discovery of America was followed by possibly the greatest demographic disaster in the history of the world." Research by some scholars provides population estimates of the pre-contact Americas to be as high as 112 million in 1492, while others estimate the population to have been as low as eight million. In any case, the native population declined to less than six million by 1650.
In this collection of essays, historians, anthropologists, and geographers discuss the discrepancies in the population estimates and the evidence for the post-European decline. Woodrow Borah, Angel Rosenblat, William T. Sanders, and others touch on such topics as the Indian slave trade, diseases, military action, and the disruption of the social systems of the native peoples. Offering varying points of view, the contributors critically analyze major hemispheric and regional data and estimates for pre- and post-European contact.
This revised edition features a new introduction by Denevan reviewing recent literature and providing a new hemispheric estimate of 54 million, a foreword by W. George Lovell of Queen's University, and a comprehensive updating of the already extensive bibliography. Research in this subject is accelerating, with contributions from many disciplines. The discussions and essays presented here can serve both as an overview of past estimates, conflicts, and methods and as indicators of new approaches and perspectives.