She could have to replace Biden as VP after Jan 20,
or she would have to remain SoS, hope Obama and Biden stepped down, and hope Boehner declined or stepped down, and the same with the Senate pro tempore.
As SoS, she is 4th in line:
Speaker of the House,
Senate pro tempore [currently Daniel Inouye (D-Hi)],
Attorney General, ...
So let me see if I have this straight. We've got
Obama - Happy (aka Gay)
Biden - Dopey
Boehner - Bashful
Hillary - Grumpy
Not quite. There is a vacancy in the Presidency and Vice-Presidency between noon, January 20, 2013, and when the oaths are taken. The Speaker, and Senate President, are the next two in line, but they have to resign from Congress, and take the oath as President, before they become President. So before somebody ahead of the SOS is sworn in, the SOS executes the office of the Presidency.
I'm not big on parlor games, but what if...
Akin keeps his mouth shut, Romney loses by less, but the Republicans pick up Senate seats in MO, IN, ND and somewhere. On January 19, 2013, the Republican Congress passes,and sends to BO a bill repealing Obamacare. BO announces that vetoing it will be the first act of his second term.
Speaker Boehner, at exactly noon, the next day, rapidly signs a document that says "There being a vacancy in the offices of President and Vice-President, I resign as Speaker of the House and Member of Congress, in order to take the oath as President." Boehner hands it to the Clerk of the House, who immediately time and date stamps it, and an auctioneer, who is also a Notary Public for the District of Columbia, rattles off the oath of office as President, Boehner says "I do" and then signs a document giving his approval, as President, of the bill repealing Obamacare, and just for the hell of it, an Executive Order firing all of BO's Cabinet Officers. Then the Chief Justice finishes administering the oath to BO, who begins his second term.
There would probably be the greatest constitutional crisis since the Hayes-Tilden election of 1876. But...
I think Obamacare would be repealed,and BO would have to renominate all of his cabinet officers.