This is totally not trolling, I just got the question in my head a minute ago and it seemed interesting.

Okay.

So, if a Nixon thing happened, and Cheney had to resign, who would Bush be likely to replace him with?  Now consider that answer carried forward to stage 2, when Bush has to step down as well... So Agnew and Nixon are gone, but who's Ford?

Hard to imagine it being anyone but Condoleezza.  Now that would have an interesting international impact.

"We cannot allow a mine shaft gap"

Well, if things unfolded in a parallel manner, I assume the President is able to appoint a replacement for Vice-P.  I can't think of anyone else who is both close enough to Bush that he would trust them, and strong enough in their public image that the people would.

I don't remember who takes over immediately for Cheney if he was to resign, but if Pres and VP both resign, then the next person in line is Dennis Hastert (Leader of the House of Rep) I think.

Found this after I wrote above
 

1. Vice President of the United States 
2. Speaker of the House 
3. President pro Tempore of the Senate
4. Secretary of State
5. Secretary of the Treasury
6. Secretary of Defense 
7. Attorney General 
8. Secretary of the Interior 
9. Secretary of Agriculture 
10. Secretary of Commerce 
11. Secretary of Labor 
12. Secretary of Health & Human Services 
13. Secretary of Housing & Urban Development 
14. Secretary of Transportation 
15. Secretary of Energy 
16. Secretary of Education
17. Secretary of Veterans’ Affairs 

Jordan .

But Nixon went straight to Ford, who was Senate President. I don't know who was Speaker at the time...

- - - - - - -

UPDATE:

It was Carl Albert, a Democrat. From Wikipedia :

As Speaker of the House, Albert was next in line to assume the presidency following the resignation of Vice President Spiro Agnew. As the Watergate crisis began to unfold, many believed that President Richard Nixon would resign before Congress could appoint a replacement, which would have made Albert his successor.

Albert was confronted with the question of whether it was appropriate for a Democrat to assume the nation's highest office when there was a public mandate for it to be held by the opposing party. Albert considered that he had no right to a White House that the American people had entrusted to a Republican. He thus announced that should he need to assume the presidency, he would do so only in an acting capacity, and would resign immediately after Congress appointed a Republican Vice President.

Apparently there's a 25th Amendment that allowed Nixon to choose a replacement, and Albert never had to turn down the job.

Jordan .