Analyses of genetic polymorphism data have the potential to be highly informative about the demographic history of Native American populations, but due to a combination of historical and political factors, there are essentially no autosomal sequence polymorphism data from any Native American group. However, there are many resequencing studies involving Latinos, whose genomes contain segments inherited from their Native American ancestors. In this study, we introduce a new method for estimating local ancestry across the genomes of admixed individuals and show how this method, along with dense genotyping and targeted resequencing, can be used to assay genetic variation in ancestral Native American groups. We analyze roughly 6 Mb of resequencing data from 22 Mexican Americans to provide the first large-scale view of sequence level variation in Native Americans. We observe low levels of diversity and high levels of linkage disequilibrium in the Native American-derived sequences, consistent with a recent severe population bottleneck associated with the initial peopling of the Americas. Using two different computational approaches, one novel, we estimate that this bottleneck occurred roughly 12.5 Kya; when uncertainty in the estimation process is taken into account, our results are consistent with archeological estimates for the colonization of the Americas.