There is no “assumption” in the 12th Amendment, it is definitive and final as long as there are no written objections to the certification of the votes of the Electors.
My personal opinion is that the 20th Amendment presupposes challeges to Electors that would take a President-Elect below the “majority of the Electors” threshold.
For example, at the Joint Session of Congress held on January 4th, if one Senator and One Representative had lodged written objections to Obama’s electors in California and Ohio, that would have taken him down to only 259 electoral votes which is below 270 electoral votes needed for a majority and he could not assume the office of President until those objections were resolved by Congress, if ever. He would not have “qualified” and Biden would be acting president until resolution, or if there was no resolution by noon tomorrow, January 20th to give Obama 270 Electors, Congress could have selected a president under the provisions of the 20th Amendment.
But there were no written objections.
So What? So you are concluding that the only way a President elect can fail to qualify during the time period after the electors vote and before the inauguration, is if there is an objection from one senator and one congressman? So Sorry, I can not agree with you.... That is not the way I read the 20th amendment. Using your assumption, if after the electors vote, clear evidence becomes public that definitely reveals a President elect "failed to qualify" Unless there is an objection, the office of the President can be constitutionally usurped? I don't think so.
I believe during this time period, a president elect can fail to qualify many different ways....For example.... 1)Assuming room temperature. 2)Mental illness. 3)Committing a crime. 4)Treason. 5)Evidence showing that Forged documents were used to hide ineligibility. (Obumer) Look at congress.... Not one makes an objection!! Yet The evidence is very clear that a crime was committed. I believe a grave situation like this was anticipated and that is why they use the words ".... failed to qualify.