The worst electoral defeat ever suffered by Franklin D. Roosevelt was his 1914 attempt to win a US Senate seat from New York. Some people in the Wilson administration (where FDR was serving as Assistant Secretary of the Navy) thought it would be a good idea for him to challenge Tammany Hall--and the ambitious young man readily agreed. FDR would probably have done better to consult Louis Howe
https://en.wikipedia.org/wiki/Louis_Howe first (Howe once said he had accompanied FDR to Washington precisely to talk him out of snap decisions...) but Howe didn't learn about the decision until FDR had committed himself. So the ever-loyal Howe left for New York to run FDR's campaign. For the first time, the nomination was going to be decided by a primary, and the election by the people, not the legislature. FDR and Howe probably hoped that Tammany boss Murphy
https://en.wikipedia.org/wiki/Charles_Francis_Murphy would support either some hack or the very controversial William Randolph Hearst. But Murphy was too smart to do either of those things, and instead chose James W. Gerard, Wilson's ambassador to Germany. It was a shrewd move: Gerard was both well-respected and rich, and had been a major contributor to Wilson's presidential campaign (which of course was how he got his post in Berlin...) So any chance of the Wilson administration backing FDR was dead. Gerard crushed FDR 62.08%-29.64%
http://www.ourcampaigns.com/RaceDetail.html?RaceID=164609 (This was a worse defeat for FDR than his 1920 defeat--not only in percent of the vote, but because in 1920, nobody blamed him for the Democratic ticket's defeat, since he was simply Cox's running mate. In 1914 there was nobody to blame but himself.) Gerard went on to lose in November to Republican James W. Wadsworth by 47.04%-42.06%.
http://www.ourcampaigns.com/RaceDetail.html?RaceID=36437
Is there any way we can get FDR elected US Senator in 1914? It is certainly a long shot at best. You would probably need to have Murphy die a decade early, and someone much less sagacious head Tammany Hall, so they would pick a weak candidate. Yet even if nominated, FDR would be an underdog in November, though perhaps as a Roosevelt, an Upstater, and an outspoken "reformer" he could get some votes that went for Wadsworth or the Progressive candidate Colby in OTL.
Anyway, suppose FDR defies the odds and does indeed get elected US Senator in 1914? Maybe with a position like that, he could get not the vice-presidential but the *presidential* nomination in 1920--and then lose so heavily that he would never be considered for the presidency again...