Does the vote for President In America have to be on one day?

The US constitution says the below:

“Clause 4: Election day
The Congress may determine the Time of chusing [sic] the Electors, and the Day on which they shall give their Votes; which Day shall be the same throughout the United States.
Congress sets a national Election Day. Currently, Electors are chosen on the Tuesday following the first Monday in November, in the year before the President’s term is to expire. The Electors cast their votes on the Monday following the second Wednesday in December of that year. Thereafter, the votes are opened and counted by the Vice President, as President of the Senate, in a joint session of Congress.”

It seems to me since we allow early voting that the election day for the popular vote does not have to be on one day, but rather the reporting of the vote by each state needs to be done by that day. Or, even more important the day in which the electoral vote must be submitted.

How do you interpret what is written concerning the matter in the constitution?

What prompted me to look it up is people discussing delaying the vote in the states that have been affected by the storm. I remember during the Bush Gore vote a reason to consider extending a vote, or revote was natural disaster under state law. Something like that. I can’t remember exactly. The movie Recount shows the Republican women in charge of the vote happy she doesn’t have to make an exception since there was not a natural disaster.

Do you think there should be a delay in voting in the affected states?