There are a few cases of this, but here, I'll talk about the earliest.

In the 1778 Treaty of Fort Pitt, the Lenape (Delaware) residing in eastern Ohio were invited to (eventually) form a state and have representation in Congress:

And it is further agreed on between the contracting parties should it for the future be found conducive for the mutual interest of both parties to invite any other tribes who have been friends to the interest of the United States, to join the present confederation, and to form a state whereof the Delaware nation shall be the head, and have a representation in Congress [...]

Signing for the Lenape were Koquethagechton (White Eyes), the Principal Chief, Gelelemend (John Killbuck Jr) who had previously been passed over for Principal Chief but would soon hold the position, and Hopocan (Pipe), the War Chief.

The Treaty of Fort Pitt fell about fairly quickly though. The US accused the Lenape of not living up to their obligations in the war against the British; the Lenape accused the Americans of altering the treaty after the fact and that all they had agreed to was to allow the Americans safe passage through their territory. In November, less than two months after signing the Treaty and before Congress had ratified it, Koquethagechton was escorting an American force to Detroit. According to official reports at the time, he contracted smallpox and soon died. However, it was later revealed that he had been murdered by the American militia and his death-covered up. Relations between the US and the Lenape continued to break down with US.

In the spring of 1781, the Americans razed the Lenape capital, Coshocton, and the neighboring communities. That autumn, the pro-British Lenape Faction, mainly traditionalist members of the Wolf Clan, forcibly evacuated the remaining neutral Christian Lenape from the area and re-settled them in northern Ohio. When supplies dwindled, nearly 100 Christian Lenape returned to their old village, Gnadenhutten (a Moravian mission village that had previously been spared in the first attack), to gather the harvest left behind. While at Gnadenhutten, they were captured by a Pennsylvanian militia and systematically executed with blows to the head and scalping, with only two boys escaping the slaughter.

The Gnadenhutten Massacre outraged Native Americans and Euroamericans alike, though the militia was never officially punished and was widely praised by US citizens in the frontier. The particularly harsh treatment that the American captives of the Crawford Expedition received, including the lengthy torture and burning of Colonel William Crawford himself, was retaliation for the Gnadenhutten Massacre. And while the Americans would remember Crawford's execution as a prime example of Native savagery for decades, Native peoples would remember Gnadenhutten has a prime example of US savagery too.

After the Revolution, neither the Lenape and their allies nor the US had any interest in joining up with each other. After the Revolution, the Lenape were among the founding members of the Western Confederacy, which declared itself an independent nation with the Ohio River as its border (basically, it was region that the US at the time recognized as the Northwest Territory, with alliances extending southward). The Western Confederacy sent a letter to Congress, informing the US of their intent, requesting that the keep US surveyors and settlers on their side of Ohio, and proposing a peace conference. The US tried to ignore the Western Confederacy, but that's a story for another time.

Also, here's a related post about Gelelemend / John Killbuck Jr.