Well, first you'll want to consider that the indigenous people of the Americas are nowhere near a homogenous unit. The differences in culture, language and societal structure between a Pequot village in Connecticut and a Blackfoot band in Montana are (speaking unscientifically) as great as any between Eurasian peoples. Even neighboring tribes with related languages, e.g. the Ute and Comanche, often perceived themselves as distinct enough to have tribal rivalries stretching back as long as any source can tell you.

The reason people presuppose Native American homogeneity is because of a concept essentially foreign to precontact Americans: a racial division between 'Indians' and everyone else, but especially Europeans. Once you bring that concept in, and make it visible enough to trump tribal allegiance, then you start to form a possible 'Indian nation'. This is essentially what happened in the confederacies that formed to combat Spanish and English (and later Mexican and American) colonization - most famously those of Popé and Tecumseh. Tecumseh's War in particular, part of the War of 1812, was based on the idea of Indian unity and the formation of a pan-American confederacy. This is built into the religious revival movement that Tecumseh belonged to, that of his brother Tenskwatawa. Such religions were very influential in extending the view of Native American unity.

So the idea of Native Americans attempting to 'unify' in precontact times is pretty problematic. Nonetheless, there are signs of certain local unifying cultures building up, most famously the Iroquois. Scholars now generally believe that the Iroquois Confederacy was created before European contact. Suggested dates vary, but the late 14th-15th centuries are commonly hypothesized. Also called the Five (now Six) Nations, this confederacy was an alliance, bound up in ritual, between five tribes of the Iroquoian groups on the southern side of Lake Ontario; the sixth tribe, the Tuscarora, were added much later, in 1722.

From that we can see that the Iroquois Confederacy was at least in principle open to adoption of other tribes; but in practice the bonds were very tight, and extended only to Northern Iroquoian tribes in that particular location. Their success post-contact is attributable more to their location on the fur trading routes, the abundance of fur within the area, and their aggressive means of acquiring trapping land, rather than their unifying culture.

Other than the Iroquois - and that a marginal case - you won't find good examples of nations dominating like that in America north of the Rio Grande, because as I've said above the concept of a 'nation' wasn't one in common circulation in most areas. 'Tribal' allegiance was much more common. If you're willing to look south, however, the Aztecs and Inca are great examples of cultural as well as military empires.

As /u/quinnipiacker, the short answer is no. No one was in particularly primed position to become a singular regional power like Rome or China.

Now, there were several strong polities in the area that's now the US, and of those, some where on campaigns of conquest when Europeans showed up. In the extreme southeast, the Calusa were busily conquering southern Florida. Their capital was just south of Charlotte Harbor. When the Spanish arrived, they had the Everglades, the Keys, and the east coast of Florida as far north as Cape Canaveral under their influence. A bit closer to home, they were fighting a prolonged war against the Tocobaga for control of Tampa Bay.

In Virgina, the Powhatan Confederacy united some thirty small polities around Chesapeake Bay through a combination of diplomacy, threats of violence, and applications of violence. By the time the English established a permanent settlement in Virginia, the Powhatan had risen from a small confederacy of five towns in the vicinity of Richmond, Virginia, to cover the entirety of modern Virginia from the fall line eastward, including the southern part of the Delmarva Peninsula. At the north end of Virginia, they were taking over polities that formerly been tributaries of the Piscataway (whose capital of Mayone in the vicinity of modern Washington, DC).

In the southern Applachians, Coosa was the largest unified pre-Columbian polity north-of-Mexico, as far as we can currently confirm. It stretched some 300 miles along the modern Tennessee-North Carolina border down into Alabama. It had several tributary polities that rebelled from time to time and had to be remind to pay up when tribute was due with a show of force. While Coosa itself (located in northern Georgia) only became the capital around 1450, it's quite possible that it represents a capital-transfer from Etowah, which dominated the area in the 1300s, since Coosa gains an elite housing district around the same time Etowah loses its own. The people in charge may have just moved. There were several other large late Mississippian polities around Coosa that were variously rivals and allies depending on the specific circumstances. These included Tuskaloosa (central Alabama), Cofitachequi (South Carolina), Apalachee (Tallahassee), and a rather poorly known one based around Mobile Bay.

At the time of European contact, the southern Mississippi valley was dominated by the Plaquemine culture. While the Plaquemine culture probably wasn't a single political entity, it does appear to have been linked in a network of powerful military alliances led by Quigualtam, who personally commanded a fleet of some 100 war canoes (the largest class of which carried 70+ men). While Quigualtam and his people were Natchezan speakers, his dominion extended over Tunica-speakers as well, who paid tribute to him. When the Spanish tried to make him come and pay tribute to him, he respond that on the contrary, everyone of whom he had knowledge paid him tribute - either willing or by force. If the Spanish came to him in peace, he'd welcome them; if they meant to have war, well, Quigualtam would be waiting for them all the same. As the last member of Quigualtam's alliance to drive the Spanish out of the Southeast watched the survivors of de Soto's expedition sail down the last stretch of the Mississippi, he shouted that the Spanish should be glad that they (Quigualtam's alliance) did not have ships large enough to follow them across the sea.

/u/quinnipiacker mentioned the Iroquois. The Haudenosaunee (Iroquois Confederacy) was a major player in the colonial era and during the Beaver Wars of 1600s, pushed their territory westward to include most of the land between the Great Lakes and the Ohio River. However, the specific reasons for that westward push are closely tied to European contact. At the time of European contact wasn't in any better position for regional conquest than any of the other powerful confederacies in the area like the Wendat, the Erie, the Shawnee, the Susquehannock, or the Mahican. The Haudenosaunee might have had an ideological advantage since their Gayashagowa encourages spreading the Great Peace to as many nations as possible, and authorizes the use of force to do so against nations that repeatedly reject the Great Peace. But plenty of other nations conquered without needing a specific legal provision granting them permission to do so, so that clause in the Gayanashagowa isn't necessary for a would-be imperial power.

Just to round this out and give you the perspective from the other side of the continent, the answer is a resounding no. There were, for the most part, no polities in the northwest that are comparable to the eastern woodlands discussed by /u/Reedstilt. Among the natives of the far north, (Haida, Tlingit and Nu-cha-nulth [formerly Nootka], there appears to be some evidence of leadership at the level of settlement. There existed clans and among some, moieties. However, for the vast majority of NW native peoples, the primary and only political entity was the household. A household or alliance of households might quarrel or war with another, or engage in slave raids together. Indeed, warring and slave raids were well documented during the Porto-historic period.

Even the notion of "tribe" is problematic. For the most part tribes have been designated as linguistically homogeneous groups. As Kroeber points out in The Handbook of California Indians, people of far Northern California held in common virtually all cultural traits except language and were notoriously fluent in many languages. Thus ones allegiance was not necessarily to others of the same linguistic class (what anthropologists called tribes), but could cross language groups to include people related to you through marriage or other connections. So, for the northwest, similar to the discussions by /u/quinnipiacker and /u/Reedstilt there was no indication of any movement toward unification above household or in some cases, settlement in late prehistory. Edit: grammar