It would have been piecemeal State by State. Depending on who came into power some States would have been faster to succumb than others, but in the end they would all have fallen. It's the nature of power.
Over time they all become corrupt. If the Anti-Federalists had won we might be in a different pickle, but it would still have been a pickle. At least we have the positive statement of the Bill of Rights. When that goes we're screwed.