Having debated a number of different executive structures for the federal government at the Constitutional Convention, on September 1, 1787, the concept of the office of the Vice President was first put forth by a committee headed by New Jersey delegate David Brearly as the sixth of a nine proposal recommendation, almost all of which were ultimately incorporated into the final draft of the document.
On Thursday, September 6, the delegates adopted the concept of a Vice President, agreeing by 10-1 vote that the President and Vice President would each be chosen to a term of four years (this overrode an earlier vote that restricted Presidents to a single, seven-year term). The next day the delegates voted, 6 states to 4 with one abstention, to let Congress determine who shall act in cases of a disability of both the President and Vice President - in effect saying nothing to the issue.
In fact, the Vice Presidency as a whole was an afterthought, incorporated haphazardly into the Constitution during the convention's closing weeks. What little debate the Vice Presidency did generate implied that the Vice President was to preside over the United States Senate, and that, in case of a presidential vacancy or incapacity, he would act as President. But in the document itself, the founding fathers would forever cloud that intention in what would become Article II, Section 1, Clause 6:
"In case of the Removal of the President from Office, or of his Death, Resignation, or Inability to discharge the Powers and Duties of said Office, the same shall devolve upon the Vice President, and the Congress may by Law provide for the Case of Removal, Death, Resignation or Inability, both of the President and Vice President, declaring what Officer shall then act as President, and such Officer shall act accordingly, until the Disability be removed, or a President shall be elected."
Eight words from the above: "...the same shall devolve upon the Vice President," would cause the nation to suffer leadership paralysis on at least two occasions, and possibly a dozen others to lesser extent. What did the phrase mean? Did it mean the Vice President would succeed to the office of President, or merely to its powers and duties? And what exactly constituted an "inability to discharge" the powers and duties of the presidency? How would an incapacitated President, once recovered, resume his office?
These and other questions went unanswered by the convention, and as a result in several instances constitutional clarity could have resulted in at least a temporary transfer of executive authority - but didn't. And the first of these instances came much sooner than anyone could have possibly expected.