Well, with no/less precedence of cooperation with the locals as equals, you'll end up with more hostile relations to the natives. If it gets bad enough, you might see them siding with the French against the colonists, which would wipe out Franklin's invitations of the Cherriky, Semmynole, and Irrakwa to the Continental Congress.
No Congressional invite implies no recognition, which in turn implies no Statehood under the Articles of Confederacy. In addition, the lack of Irrakwa and Cherriky support (in the north and south respectively) would probably lead to a longer war, the Founding Fathers might have lost, and the USA would almost certainly be smaller than it is today.
After that, the butterflies get too numerous to count really. But, assuming there is a USA, no 'Three Brothers' indian states would also mean a lack of peaceful examples for incorporating natives into the Union. Slower, more militant expansion, less intermarriage, more racial disharmony. Impact on the Manumission Strife in the 1840s is hard to say - indians were on both sides of the various riots and debates there. But without a third 'party' things could drag on for longer.
A US occupied by internal issues wouldn't have the time or energy to intervene in the Mexican troubles, and certainly wouldn't have the resources for involvements beyond our shores.
Sounds depressing - not a puritan myself, but those first conversions did help steer relations to a more equitable footing. I would hate to see the US will policies similar to those followed in Tasmania.
(OOC - Decided to be optimistic for once...)