Let's imagine in '33 FDR was killed by Zangara, eventually Eleanor would have decided to react by launching herself in a political career, as for Senator or Governor of New York maybe? I would like to inquire over this particular, probably unnoticeable so far, aspect of the dead FDR pods.
EDIT: forgot in the thread title to add the last word "career".
I would think that, as a woman at the time, her political career would be pretty limited. Could she get elected as Senator for New York, say? I think so - but that'd be about the best she could do.
I think a better route if you want her prominent would be to have FDR shot - but not killed. FDR uses Eleanor as his spokesperson, especially while he's hospitalized, and she gains a large national prominence. Then FDR doesn't run for a 3rd term in 1940, due to much poorer health, and Eleanor runs instead.
Most of the world sees this as 'a trick to evade the 2 term limit' or 'being FDR's puppet/proxy', but she's still elected due to people not wanting to switch horses in midstream with a war coming, and when FDR dies in her first term, she continues running the war effort and wins a second term in '44 on her own merits.