Clauses 2 and 3 of Section 1, Article II of the US Constitution describe how the president is chosen:
“Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress; but no Senator or Representative, or person holding an Office of Trust or Profit under the United States shall be appointed an Elector.
The Congress may determine the Time of chusing the Electors, and the Day on which they shall give their Votes; which Day shall be the same throughout the United States.“
The Constitution thus identifies two authorities responsible for the administration of presidential elections, state legislatures and Congress. All 50 states have legislated that Electors are chosen through a popular vote, and since 1845, Congress has set the “time of chusing Electors” as the first Tuesday after the first Monday in November.
That’s how presidents are chosen. Changing Election Day would require an act of Congress, and even then, the Constitution specifies that a presidential term is limited to four years, and that a term ends “at noon on the 20th day of January.” If, for whatever reason, there is no president- and vice-president-elect, Congress provides that the vacancy shall be filled by an “acting president” with the Speaker of the House first in the succession.
Changing the way that Electors are chosen would require acts from the state legislatures. If a state fails to choose electors by Nov 3rd, 2020 this year, Congress requires that “electors may be appointed on a subsequent day in such a manner as the legislature of such State may direct.” In other words, state legislatures would have to deny federal law by postponing the election, and deny the authority of their own constituents, if they sought to choose Electors by some other means.
US Presidents have only the powers granted to them by the Constitution or acts of Congress. It is settled law that even the extraordinary powers granted to the president during times of war do not extend to domestic affairs. As a result of the Constitution, Congressional authority, and settled law, there is no express or inherent power for the president to delay or postpone an election. This is why no president has ever delayed or postponed an election.