The First Party System of Federalists vs. Jeffersonian Republicans would have to dissolve at some point, but the Federalists could easily have lasted longer given a variety of PODS. Had Hamilton made the smart choice and not duelled Burr, he could have run in 1804 and 1808 as the head of a galvanized, unified Federalist Party. It's doubtful that he'd win, but he could make sure the Federalists remain an effective political force for the next 20 years until the upheaval of the Jacksonian era.