Congress can change the date of the election if they fear a storm is coming, but the entire nation must vote on the SAME DAY (and only one "day") across the country.
The phrase "which Day shall be the same throughout the United States" refers to the "Day on which they [the Electors, e.g., the Electoral College] shall give their votes." So, the Electoral College electors in each state must vote on the same date; the clause does not, strictly speaking, require election day (e.g., the "Time of chusing the electors") to occur on the same day nationwide.
-PJ