“U.S. Constitution: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. “
Pay a little bit of attention to what it says: it says that *the electoral college* must cast all their *electoral votes* on the same day (in the early days, when state legislatures typically picked the “electors”, it would have been bad if the states could play waiting games and see who the other states were going for).