There's presumably a statute somewhere that covers this....though, after Jacob's suggestion, Robert Gates is another quasi-plausible result. Depends on the timing, though.
Obama's plans to nominate someone for a cabinet position wouldn't have any constitutional standing though. If Obama is never sworn in as President, his preference for Defense Secretary wouldn't matter.
Gates is already SoD and will not need renomination. If Obama, Biden, Pelosi, and Byrd all kick the bucket so that there is not time for the Senate to select a President pro tem, or the House to elect a Speaker before noon on January 20, then under the current law, we'd have a very curious situation. The senior eligible cabinet officer remaining would become President at noon on January 20.
Peculiarly if Bush and Cheney also die at that time, we'd need two cabinet officers someplace safe to maintain the order of succession. The first would take office immediately, but would leave office at noon on January 20 to be succeeded by the next most senior cabinet officer.