What Would Happen?

[zorkpolitics]

This is the order of succession already includes two people who ar eineligible becaus ehtey were not born int he US:
The Vice President Richard Cheney
Speaker of the House John Dennis Hastert
President pro tempore of the Senate Ted Stevens
Secretary of State Condoleezza Rice
Secretary of the Treasury John Snow
Secretary of Defense Donald H. Rumsfeld
Attorney General Alberto Gonzales
Secretary of the Interior Gale A. Norton
Secretary of Agriculture Mike Johanns
Secretary of Commerce Carlos Gutierrez (ineligible)
Secretary of Labor Elaine Chao (ineligible)
Secretary of Health and Human Services Mike Leavitt
Secretary of Housing and Urban Development Alphonso Jackson
Secretary of Transportation Norman Yoshio Mineta
Secretary of Energy Samuel Bodman
Secretary of Education Margaret Spellings
Secretary of Veterans Affairs Jim Nicholson
Secretary of Homeland Security Tom Ridge

If all 17 are dead or ineligible,  the House or Senate would vote for a new Speaker or President Pro Temp, thus refilling the order sussession.   There is no provision for a special election.

[zorkpolitics]

Another question about the original scenario.  The vice-president becomes president as soon as the president dies.  Is he included on the list of presidents even though he is never sworn in?

David Rice Atchison was President for 1 day in 1849 because Zachary Taylor refused to be sworn in on a Sunday and he is never mentioned as a President.

Apparently Atchinson spent all of Sunday in bed sleeping off the previous night's cellebration, so he missed his 1 day Presidency.