How might the existence of a clear, powerful external foe affect American society, politics? More centralization? What about the whole slavery thing?
I would say that the existence of a big continental power in North America blocking US expansion to the left bank of the Mississippi is far more decisive than the friendly or hostile character of this big power.
It does just butterfly away what was the main incentive for european migrants to keep flowing to the US : opportunity for all to have "free capital". The "free capital" would be spread on "only" 2.5 million square kilometers instead of 9.6 million. So many european migrants will directly go to the place where there are bigger opportunities.
This means the US will remain an american atlantic power.
This also means that such a US will never be able to proclaim (less even implement) its OTL Monroe doctrine.
This means there may come a time, by the late 19th century, where a strong socialist movement may emerge as the question of social inequality and poverty can not find a solution in the pursuit of the frontier.
This means a Lincoln-like character will probably never be able to prevent secession of the southern States if they want to and that the US will not be able to take the path of building a big federal government (It took decades but North victory in the civil war was a prerequisite).