Amendment 12 paragraph 2
The President of the Senate shall, in the presence of the Senate and House of Representatives, open all the certificates and the votes shall then be counted;
It doesn't say when those votes are counted just done by the President of the Senarte (which is still the VP)
Amendment 20 Section 2
The Congress shall assemble at least once in every year, and such meeting shall begin at noon on the 3d day of January, unless they shall by law appoint a different day.
Basicallyy this is the only day out if the Year they have to meet and by congressional Rules, law antraditionon they elect Their leader and then have the sitting VP certiify and count the Electoral Votes on this day and just like any other election the results aren't official till the votes are counted.
Back to Admendment 12 it goes on to say what will happen during the Counting Which as I said is on the third of January
The person having the greatest Number of votes for President, shall be the President, if such number be a majority of the whole number of Electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately
Which as I have stated is the third of January. Becuause the tie is not official till the votes have been counted
Adment 12 Continues on
, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote; a quorum for this purpose shall consist of a member or members from two-thirds of the states, and a majority of all the states shall be necessary to a choice. And if the House of Representatives shall not choose a President whenever the right of choice shall devolve upon them, before the fourth day of March next following, then the Vice-President shall act as President, as in the case of the death or other constitutional disability of the President.
So the Way I read it it is January 3rd