An old soc.history.what-if post of mine:
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"That leading Federalists opposed to Adams did not consider the [no-third-term] rule absolutely binding is evident from their attempt in 1799 to persuade Washington to accept a third term..." Richard P. McCormick, *The Presidential Game: The Origins of American Presidential Politics* (New York and Oxford: Oxford University Press 1982), p. 245.
No doubt it is extremely unlikely that Washington would accept--but suppose his health had been better, and the Hamiltonians had persuaded him: "General, this is different from 1796. This time only you can save the nation from the Jacobins [i.e., Jefferson]. Yes, we know you said in 1796 that you would not be a candidate again, but [anticipating TR in 1912] when a man says at breakfast in the morning, 'no thank you, I will not take any more coffee,' it does not mean that he will not take any more coffee to-morrow morning, or next week, or next month, or next year."
So Washington once again reluctantly decides he must accept his country's call. What next? Obviously he is not going to get the office without bitter opposition. After Jay's Treaty, viewed by Republicans as a sell-out to the British, Washington was anything but a non-controversial, non-partisan national hero; one Republican toast in 1796 was "A speedy death to General Washington." In his retirement, he endorsed the Sedition Act, no doubt largely because of resentment of the Republican slanders about him. Still, he is George Washington, and has far more prestige than any other possible Federalist candidate, including Adams. If Adams insists on remaining a candidate, the split in the Federalist ranks between Washington and Adams presumably assures Jefferson's victory. But what if Adams sees the hopelessness of the situation and simply gives up, leaving Washington and Jefferson to fight it out?
https://groups.google.com/d/msg/soc.history.what-if/QFr8-CeL0t4/z3_IdVRUkkwJ