What Would Happen?

[True Federalist (진정한 연방 주의자)]

However, the line of succession is only 17 people deep,
VP
Speaker
PPT
14 of the heads of the Executive Departments (Secretary of Homeland Security has not yet been placed into the line of succession due to disagreements over where to put him and the perceived low priority of doing so.)

In the given scenario it could well become a race to see which House gets an elgible person in place as either Speaker or PPT.

[True Federalist (진정한 연방 주의자)]

zorkpolitics, as I already pointed out, the order of Presidential succession (contained in 3 USC 19) has not yet been amended to include the Secretary of Homeland Security.  There is a dispute over whether to place the Secretary at the end of the list or after the Attorney General in the Presidential succession list and over whether to clean up some other provisions of section 19 of title 3.  A bill passed the Senate in the last Congress but not the House.  It has been reintroduced as S.442 and is currently in committee.  It would place the Secretary of Homeland Security after the Attorney General and make no other changes, but it is not yet law.

[True Federalist (진정한 연방 주의자)]

A quick search of Thomas shows that there are 4 bills, all currently stuck in commitee going nowhere to add the Secretary of Homeland Security to the presidential secession list.  In bill number order they are:

S. 442
This bill has the same text as one which passed the Senate in the 108th Congress, but failed to be passed by the House.  All it does is place the Secretary of Homeland Security after the Attorney General in the secession list.

S. 920
Is a more ambitious bill, and if I thought it had any chance of passage would help explain the excessive controverst over Mr. Bolton.  It makes its additions to the end of the list after the Secretary of Veterans Affairs, but in addition theo the Secretary of Homeland Security it would add in order the Ambassadors to the UN, to Great Britain, to Russia, to China, and to France.

In addition it provides that if a cabinet officer gets to act as President, it only on a temporary basis until the Speaker or the President pro Tem accepts the office of President or the President or Vice President is no longer unable to perform their duties.

Then it adds some legally meaningless sense of the Congress language that suggests that it would a good idea f political parties when they nominate a President and Vice President should also decided who their electors will vote for in the case of something unfortunate happening to one or both of the candidates before the electors vote.

Finally, it adds more sense of the Congress mumbo-jumbo to suggest that it would be a good idea for the outgoing President to submit the cabinet nominations of the President-elect on January 3 so that it would be possible for for them to take office on January 20 with the incoming President.

H.R. 1455
Besides adding the Secretary of Homeland Defense after the attorney general a la S. 442 this bill also makes the Department of Homeland Security one of the listed Executive departments in 5 U.S.C. 101.

H.R. 1943
This is the exact same bill as S. 920.