And even if the election was delayed, Trump's and Pence's terms would still end at noon on January 20, 2021. If no election has been held by that point, the Speaker of the House would assume the powers of the presidency under the Presidential Succession Act.
This assumes, of course, that the elections for the House, or at least some of them, manage to go forward even if the full presidential election does not. The Speaker, however, is not constitutionally required to be a member of the House.
There is at least a colorable argument that the designation of Speaker outlasts any particular House (this would depend on House rules, which, of course, could be changed).
If the position of Speaker is vacant, next in line is the President pro tem of the Senate. In the event of a delay in Senate elections, the Senate would consist of the 2/3 of the Senators who are not up for re-election. (The terms of the other 1/3 having expired.)
Since 23 seats held by Republicans are currently up in the election, and only 12 seats held by Democrats, that truncated Senate would be in Democratic control, so the President pro tem would be a Democrat.
The point is, no matter who ultimately ends up filling the vacancy, it will not be Trump, and will almost certainly not be a Republican. In the absence of an election, Trump hasn't been legally re-elected, and the presidency will become vacant at noon on January 20, 2021.
In short, an election delay has no benefit to Trump. If he wants to hang on to the presidency, he has every incentive to make sure the election happens as scheduled.
A few more thoughts in response to some comments. Senate vacancies (unlike House vacancies) can be filled temporarily under the 17th Amendment by state governors. But not every state has authorized its governor to do so, and some states have restrictions on selections.
So some, but not all, of the Senate vacancies could be temporarily filled in this manner. It's not clear what the partisan breakdown of this would be, although I believe it could still end up on the Democratic side. But there a lot of variables.
There is a significant question over the constitutionality of the Presidential Succession Act. Article II allows Congress to designate which "Officer" shall act as President in the case of a vacancy.
Some scholars, notably Akhil Amar at Yale, have argued that "Officer" refers only to executive branch officials, and that including the Speaker of the House and the President pro tem of the Senate in the line of succession is unconstitutional. Would a court agree?
It's hard to know. I suspect the Supreme Court would be disinclined to issue such a ruling in the midst of what would already be an exceptionally chaotic situation. But if the Court did so rule, the next in line would be the Secretary of State.
Either way, the Twentieth Amendment is crystal clear: "The terms of the President and Vice President shall end at noon on the 20th day of January." Even a Trump-friendly Supreme Court cannot make this language go away.
If Trump is not lawfully re-elected by then, his term is over and someone else will be exercising the powers of the President of the United States at 12:01 pm on January 2021.
