Technically, as Sec of State Hillary is 5th or 6th in line for the presidency.
Irrellevant. If Obama were Considered to have somehow been ineligible, but still Considered to have been President, and then was removed, the 25th amendment provides:
In case of the removal of the President from office or of his death or resignation, the Vice President shall become President.
Section. 2. Whenever there is a vacancy in the office of the Vice President, the President shall nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress.
Thus Biden would nominate a new VP.
But I don't see how someone not eligible could be considered to *be* President. Thus the "fails to qualify" language of the 20th amendment would control, The VP would act as President until a President could be qualified, (procedure for that is in the 12th amendment) but would revert to his role as VP as soon as a President was qualified.