One person simultaneously prez and veep

[Will F.D. People]

There is a school of thought that the original framers of the Constitution did not intend the Vice President to actually become President upon the death of the President. Instead, they intended the Vice President to assume the duties of the President but to remain Vice President. So yes, someone could be both President and Vice President at the same time.

Artice II, Section 1:

In Case of the Removal of the President from Office, or of his Death, Resignation, or Inability to discharge the Powers and Duties of the said Office, the Same shall devolve on the VicePresident, 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.

This does not say the VP becomes the President when the President dies; it says that the powers and duties of the President devolve to the VP. If there is neither a President nor a Vice President, Congress may be law determine who is Acting President.

From Article I, Section 3:

The Senate shall choose their other Officers, and also a President pro tempore, in the Absence of the Vice President, or when he shall exercise the Office of President of the United States.

Again this implies that when the President has died, the Vice President is still Vice President, but holds the powers normally held by the President. It could have said the the President pro tempore is for the case where the office of Vice President is vacant for any reason, but it does not.

Apparently when William Henry Harrison died -- the first president to die in office -- John Tyler insisted on being sworn in as President and refused mail addressed to him if it called him the "Acting President". He established the precedent that Vice Presidents actually become President upon the death of the President and don't just assume their powers.

The last time this was really important was in 1963 when President Kennedy was killed. It turns out (accoring to "The Death of a President" by William Manchester) that no one knew what the presidential oath of office was, and it was felt important by the Johnson party that LBJ actually take the oath of office as soon as possible. (The oath is actually given in the Constitution.) Manchester points out that it is reasonable to think that Johnson did not have to take the oath at all, since he had already taken the oath to be Vice President, so by the Constitution the duties of the president had lawfully already been transferred to him.

[Will F.D. People]

I'm not certain, but before the 12th Amendment, every Elector had two votes.  The could cast both for one candidate.

In the Constitution it says in Article II, Section 1, Clause 3 (since superceded):

The Electors shall meet in their respective States, and vote by Ballot for two Persons, of whom one at least shall not be an Inhabitant of the same State with themselves.

I would interpret this to mean that an elector could not have voted for the same person twice. I would interpret this to mean that an electorwas required to vote for two distinct persons.

As for whether it was generally accepted that the Vice President merely acted as President upon the death of the President rather than actually becoming President, here is an interesting article:

http://www.suite101.com/article.cfm/presidents_and_first_ladies/31466

While researching this I found another interesting tidbit that Tyler was the first President to have a veto overridden.

One thing I do not find in the Constitution at all is something that says when a VP becomes President, his term lasts until the end of the person whom he took over for. Article II, Section 1, Clause 1 says the term of office for a President (and Vice President) is 4 years. So if a VP becomes President, you could argue that he gets his own 4 years.