[El Gato]

Who gets impeached is who holds the office of President.

That's not what the Constitution says, it says

The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.

Art. II, Section 4.

It also says:

No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President;

So how can someone not eligible to the office "hold" it? By that argument, someone could walk in off the street and "hold" the office. I mean if you're willing to disregard one requirement, why not a couple more of them? Maybe only one requirement. The guy could sign a copy of the oath, be over 35, 14 years a resident, and be a natural born citizen.

Ridiculous of course, but it does follow from your position.

[KenyanBCPunkster]

No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President;

So how can someone not eligible to the office "hold" it?

Because the Twelfth Amendment clearly states who actually IS the President:

The President of the Senate shall, in the presence of the Senate and House of Representatives, open all the certificates and the votes shall then be counted;- The person having the greatest number of votes for President, shall be the President...

Obama received the greatest number of votes for President. He IS the President, and therefore "holds" that office until such time as Congress shall remove him (barring expiration of his term, etc.).

By that argument, someone could walk in off the street and "hold" the office

Not without having received the greatest number of votes for President they couldn't.