Greenberg's 1987 book Language in the Americas proposed that nearly all indigenous languages of the Americas outside Eskimo-Aleut and Na-Dene form one Amerind family, using his mass comparison method. Most historical linguists reject mass comparison as a method for establishing genetic relationships, and reviewers found extensive inaccuracies in the supporting data, so the proposal has generated lively debate but is rejected by most specialists.
What would resolve this Rigorous application of the standard comparative method, with reconstructed sound correspondences and paradigmatic morphology, to each of the many individual language families Amerind proposes to unite, verified independently of Greenberg's own cognate sets.
OpenHistorical and comparative linguisticsWikipedia: Joseph Greenberg