Article II, Section One of the Constitution states: "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." This could be interpreted to mean that the "time of chusing the Electors" needs to be on the same day throughout the United States.
Section 2 from Chapter One of Title 3 in the United States Code (62 Stat. 672, as amended - source: National Archives), reads as follows: "Whenever any state has held an election for the purpose of choosing electors, and has failed to make a choice on the day prescribed by law, the electors may be appointed on a subsequent day in such a manner as the legislature of such State may direct."
But this section does not refer to "choosing" in elections. It appears to refer to the appointment of specific electors. It would seem unlikely that any court would allow a federal code to supercede the Constitution. In fairness, we must also add that it may be possible to interpret that the clause "which Day shall be the same throughout the United States" refers only to the date the Electors cast their votes, and not to the "time of chusing the Electors."
Admittedly, this potential contradiction between the Constitution and the United States Code has not been litigated. There is a statement at the National Archives website that in the event of a tie, "federal law would allow a state to hold a run-off election," which also appears to contradict the "Day shall be the same" clause in the Constitution.
So the most accurate statement is the first statement, that such an election may be unconstitutional. Congress does not have any jurisdiction over redoing a state election. The state would not call a new election by "executive order." And the consenting candidates could not simply agree to have a new election. (According to the United States Code, the state legislature would have to ratify such an agreement.)
Copyright © 2001 by Richard Warren Field