From a reader:

If this Jonathan Alter article from Newsweek is correct, this not so great idea goes back even further.
The relevant paragraph is:
But FDR was so eager to take office that he briefly concocted a scheme whereby Hoover would appoint him secretary of state, then Hoover would resign along with his vice president, Charles Curtis. This would allow Roosevelt to be president immediately instead of waiting four long months until March 4, the date of the Inaugural in those days. (After 1933 it was changed to Jan. 20.) The gambit went nowhere.