In recent floras and online databases, Ipomoea purpurea is usually considered introduced to the United States as a whole, by way of cultivated plants originally collected in southern Mexico. Most earlier floras agree on this point as well. For instance, Gray (1878, Synoptical Flora of North America) says it is “an escape from cultivation in the Atlantic States”, although it “may be indigenous” in San Diego, California. House (1908, Annals of the New York Academy of Sciences 18: 181-263) says it is “throughout tropical America” but “cultivated and a frequent escape northward”. Wooton & Standley (1915, Flora of New Mexico) give its range as “tropical America , frequently introduced elsewhere”. Kearney & Peebles (1960, Arizona Flora), Correll & Johnston (1979, Manual of the Vascular Plants of Texas), and Martin & Hutchins (1980, Flora of New Mexico) all indicate it is introduced as well.
However, the situation is more complicated. These authors used different taxonomies than our current understanding of Ipomoea. Within the southwestern United States, what we now call “Ipomoea purpurea” was split into two species by Gray (Ipomoea mexicana and Ipomoea purpurea), three species by House (Ipomoea desertorum, Ipomoea hirsutula, and Ipomoea purpurea), three species (the same as House) by Wooton & Standley, two species by Kearney & Peebles (Ipomoea hirsutula and Ipomoea purpurea), two varieties by Correll & Johnston (Ipomoea purpurea var. diversifolia and Ipomoea purpurea var. purpurea), and two species by Martin & Hutchins (Ipomoea hirsutula and Ipomoea purpurea). All of these authors considered Ipomoea purpurea (or Ipomoea purpurea var. purpurea) to be introduced, but the others (under the names Ipomoea desertorum, Ipomoea hirsutula, Ipomoea mexicana, or Ipomoea purpurea var. diversifolia) to be native to the southwestern United States.
Austin (1990, Sida 14(2): 273-286; 1998, Journal of the Arizona-Nevada Academy of Science 2: 61-83) recognized Ipomoea purpurea without varieties and included Ipomoea desertorum, Ipomoea hirsutula, and Ipomoea mexicana within it. Most subsequent works and databases have followed Austin’s taxonomy, but apparently uncritically assigned the introduced status of Ipomoea purpurea to the entire species despite the fact that prior authors had considered many of the synonyms to be native. Austin himself was more circumspect. In 1990 he wrote: “This species is now pantropical because of cultivation, but it was undoubtedly originally Mexican. It occurs in Arizona, New Mexico, and Texas and has been introduced and/or escaped in the Great Plains, the southeastern United States and the north- eastern United States.” In 1998 he wrote that it is “pantropical, widespread in N. Amer.; probably naturalized from Mexico. This is an unusually variable species, at least in part due to human selection. Cultivated forms are always larger than wild forms, but the size of flowers and sepals may vary even in wild plants.” In both cases, he does not explicitly state that this species is or is not native to the southwestern United States.
My own experience, primarily in southern New Mexico, is that our plants neither resemble cultivated Ipomoea purpurea nor occur in the kinds of disturbed habitats that are typically associated with introduced species. During good monsoon years, it is common throughout the mountains of southern New Mexico in shrublands and woodlands, generally below the forested elevations. It can be found along roadsides but has no apparent correlation with them. I consider it to be native in the southwestern United States and can find nothing beyond its close relationship to the cultivated plants to suggest otherwise.