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The answer to the first question is "yes," with the caveat that this need not necessarily happen on the 6th, simply between the 3rd and the 20th.
The second question is trickier...
In the event of a tie, presumably unbreakable, the Vice President-elect would assume the office of POTUS on January 20. This Vice-President-elect will have been chosen either by the electors, who are not necessarily bound to have voted in accordance with the wishes of their respective populations, or by the Senate, voting as a body, not in the manner of the House of Representatives... each Senator would have one vote.
If there shall be no Vice-President having been chosen by January 20, then the Presidential Succession Act would provide for the Speaker of the House of Representatives to assume the office of POTUS, upon her or his resignation from congress. If she or he is constitutionally or otherwise unqualified for the office of POTUS, then the Act provides for the President Pro Tempore of the Senate to... you get the idea.
As for which blue states might turn traitor... there's no guesses from the Farmer... you're on your own, there.
Of course, your question is strictly theoretical, since we know the Electoral College system is fair and reliable.
Oh, wait. It's not. I forgot.
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