I have published a new piece on this question with the Washington Post, which updates the two–part series I did in August on these issues. Here is a brief excerpt:
We do not know at this moment whether President Trump will have a mild or more serious case of covid-19. But without being alarmist, there is a public need to know what the procedures would be were the president to become incapacitated in two situations: before the election or if he wins and becomes incapacitated before Inauguration Day.
The national organization for the Republican Party is known as the Republican National Committee (RNC). In the first scenario, the RNC would have the power to replace the party’s nominee for president.
The RNC has 168 members — three from each state, plus three from six territories. The RNC’s rules provide that the three members from each state cast the same number of votes that their state or territory is entitled to at the party’s nominating convention.
In some sense, that’s the easy part, given how late in the election process we are now. If there were enough time, the party would seek to put the name of its new candidate on the ballot in each state. There almost certainly would not be time to do this, particularly if the issue only arises two to three weeks from now. The states have various deadlines for when the parties must certify their candidates for the ballot. Those dates have passed. In theory, the RNC could go to court to seek an order permitting it to change the name of its candidate. But there simply would not be enough time to reprint ballots at that point. President Trump will almost certainly remain on the ballot, no matter what happens.
That makes the second scenario the more critical one. Suppose Trump wins the election, even if incapacitated, or becomes incapacitated after the election but before Inauguration Day. This situation is more complex. . . .
The bottom line is that the RNC would determine who the replacement candidate would be, should it come to that unfortunate situation. And Republican slates of electors in states the president won, because he remains on the ballot, would very likely follow the RNC’s recommendation.
But one last possibility to ponder: If the RNC were deeply divided, and Republican electors then did not coalesce around a single replacement candidate, there might not be a majority winner in the electoral college. In that case, the House would choose the president from among the top three vote getters in the electoral college. In that process, each state delegation gets one vote.
These scenarios remain highly remote possibilities at this point, of course. But these and related questions may dominate public discussion for some time.