(Disclaimer: This is a suggestion from the Steve Jackson Forums.)
Aaron Burr is mostly remembered as the man who killed Alexander Hamilton and to a lesser extent for plotting an (allegedly) treasonous adventure in the Western frontier. Fewer people know he came a hair's breadth away from being elected president over Thomas Jefferson in 1800 AD. Such an ambitious man given the reigns of power will have profound effects on the US, as will the survival of Hamilton. A more ardent ally might give Napoleon the edge he needs to triumph at Tralafagar, perhaps eventually overwhelming the British and installing his own regime in England complete with the puppet Prime Minister Lord Byron. In such a case Burr would have free reign to conqueror British Canada and Spanish Mexico (on the verge of their own revolution). On the flip side the writings of Alexander Hamilton originally founded the Federalist Party, and might be able to preserve it if he lives past 1804. Given the vagaries of that party, westward expansion might be curtailed or at least prolonged for many more decades than in our world.