In the second "What If" anthology, there is a TL that describes this happening: The Election of Theodore Roosevelt, 1912, by John Lukacs. Among other fun things, Arizona and New Mexico are one state. More importantly, Roosevelt immediately built up America's military, and just after his 1916 re-election he issued a 3-point paper to all of Europe. Quote from book:
"It was a state paper of the greatest importance. The government of the United States, Roosevelt declared, proposes one, the cessation of all hostilities in Europe and on the high seas within a month; two, the return of all armies and Powers to their state frontiers of July, 1914; three, the convocation of a Peace Congress in The Hague three months after the armistice, with the United States represented together with all other powers. None of the governments of Europe had expected such a definite proposal, not even the British. The world was stunned and startled. The cartoonist of a Hearst paper in New York drew TR, with the sun behind him, rising as Augustus Caesar over the tribes of the world."
Anyway...back to Presidents. I missed two important people in the first list: Aaron Burr and Samuel Tilden (1800 and 1876). Then, let's just say that the scenario in The Fourth Battle of Winchester (Richard McMurry) plays out. Then we have George McClellan (1864). To say nothing of politics in the Gilded Age, there could easily be four or five people in there...