Actually that comes from the 12th amendment, and the "base" Constitution, whereas my original quote was from the 20th amendment. So it actually comes before, not after the original quote.
But the 12th amendment says that the House is restricted to choosing from the top three vote getters.
First from the 12th amendment:
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, 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.
Then from the 20th amendment.
Section. 3. If, at the time fixed for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President. If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified; and the Congress may by law provide for the case wherein neither a President elect nor a Vice President elect shall have qualified, declaring who shall then act as President, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a President or Vice President shall have qualified.
Section. 4. The Congress may by law provide for the case of the death of any of the persons from whom the House of Representatives may choose a President whenever the right of choice shall have devolved upon them, and for the case of the death of any of the persons from whom the Senate may choose a Vice President whenever the right of choice shall have devolved upon them.
Remember that if an earlier amendment conflicts with a later one, the later amendment overrides the earlier one, and the base Constitution as well.
It's very clear that if the President-elect dies before January 20, then the Vice President-elect becomes President, who then would pick a VP subject to approval by Congress.
Correct so far?
However, in Section 3, it says that if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified.
If this statement is taken literally, then the use of the phrase "a President" as opposed to "the President" takes on a diferent meaning. If "THE" President-elect has failed to qualify, then there must be action taken to find someone who would qualify to be "A" President.
In other words, despite of who you or I would like to see as President, there is nothing in the Constitution that dictates who Congress must pick to replace the disqualified President-elect.
For example, let's suppose that, as a result of the Jan 16 SCOTUS conference, at least four Justices agree to hold an emergency session to hear Berg's injunction, prior to Jan 20, but here's where it gets into the gray area. and they are given several possible actions on which to vote. vote to require Obama to prove that he is Constitutionally qualified to be the President.
And, you know what? SCOTUS could very well require that he produce more evidence than just his vault birth certificate.
We have no conclusive proof that his mother was a U.S. citizen at the time of his birth. We have no conclusive proof of who was his biological father. We have a huge list of historical documents that are missing. Who really is Barack Obama? Who is even qualified to vouch for him?
Unless Obama provides the evidence that SCOTUS requests by the date requested (his vault birth certificate, for starters), he will be considered as "failed to qualify," and the Vice President-Elect would be first sworn in as Vice-President, and then, sworn in as acting President until someone is chosen to be President.
There is nothing in Section 3 that defines what would be the procedure if the President-elect was disqualified prior to January 20.
SCOTUS has the power to invalidate the entire election, if it was convinced that the DNC knew about Obama's citizenship problems and tried to hide it.