Hey, to the mods, I’m not sure if this is considered proper sourcing but I’m taking my info from Ron Chernow’s biography of Hamilton and McCollough’s bio on John Adams. So, in the musical, the election is between Jefferson and Burr, and claims that “Adams doesn’t stage a chance’, right? In actuality, the election was most certainly a contest between Jefferson and Adams. Adams had less then stellar odds, as the Federalist had been in domination of the government for years, and he had passed the very controversial Alien and Sedition acts. However, there was, theoretically, enough Federalist support in the county to re-elect John Adams. The problem was that Adams and Hamilton essentially split the Federalist Party into two wings, the pro president Adams wing and the pro-Hamilton wing. Hamilton wrote an extended and quite emotionally charged pamphlet on Adams’ faults, and pushed Federalist Charles Pinckney in the election. This split the Federalist vote and gave the opposition party ammunition to attack Adams; Hamilton was a distinct negative influence on Adams’ chance to win the election. So, Jefferson wins in 1800, but the problem comes in when you remember that at this stage, the Vice President isn’t a position that an electoral college electoral votes for. The VP is the person who comes in second place. This was changed in the 12th amendment. When the electoral college convenes to elect the president, the idea was to give Jefferson the presidency and Burr the Vice-Presidency (Burr had campaigned for Jefferson in the critical state of New York in return for the VP slot), but when the votes are totaled, the Electoral College failed to give Jefferson the nessecary majority to win the presidency. Here’s when the election of 1800 moves to the House of Representatives, where elections are decided if the Electoral college cannot produce a majority. Several ballots are held, and while Jefferson has more votes than Burr, he doesn’t have the nessecary majority to elect a president. However, eventually a Federalist changes his vote, and Jefferson is given the presidency. It’s actually a matter of contention, because some sources say that the Federalist who changed his vote did so after pressure from Hamilton switched his vote. However, while Hamilton did write several pro-jefferson letters, his influence may have or may not have been the deciding factor as to who eventually won the presidency.

TLDR: Hamilton helps Jefferson in the general election by splitting the Fed. Vote, and then again at the House by lobbing a congressman to change his vote from Burr.