Have you been following the news recently? About a week and a half ago, stories such as Lasers Reveal a Maya Civilization So Dense It Blew Experts’ Minds seemed like they were everywhere. Detailed laserlidar surveys of northern Guatemala revealed the remains of a massive Mayan settlement consisting of "about 60,000 homes, palaces, tombs and even highways". Based on this new information, they're speculating that the Mayan civilization may have had a population of 10 million people, comparing quite favorably to European nations of the time - and, indeed, to many modern nations.
So, yes, it's entirely plausible that the pre-Columbian American people could have developed nation-states, because they actually did just that in the real world.