WI Washington died before he announced not seeking 3rd term

Suppose he had some kind of accident, r caught something.

I assume John Adams takes office and is elected in 1796.

Does it prevent the two term custom
 
I don't think it would affect the traditional presidential succesion (two terms are enough)
Oh, it definitely would. The whole 'Cincinnatus' vibe of serving a period and then stepping down was a HUGE precedent and support for stable politics in the US. If he died in office, revisionists would immediately say 'Well, yes, he SAID he'd not run for a third term, but surely with the French crisis, he'd have seen we needed a steady hand on the tiller.'

No, I think without that specific example, you'll have people running for third terms on the slightest excuse.
 
A small chance someone down the line manages a 3rd term election before FDR. Very small chance.

- BNC
Jackson might have been able to go for a third term (van Buren's term was widely called Jackson's third term anyways), but he's about the only one with the health and inertia for it... and even that's a little dubious. And if van Buren thinks Jackson might scuttle the plans for his presidency by seeking a third term he may come to terms with Clay. I would think Jackson would still win, but a lot could happen in four years.
 
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