If our president had a doctorate, would he be referred to as “Dr. President” instead of “Mr. President”? Has this ever been the case? Has the first lady every been a Dr.? Were/would they be introduced as “President and Dr. [Bush]?”
Woodrow Wilson got a PhD from Johns Hopkins in 1886.
Yes, and in all my reading on U.S. history I’ve never seen Wilson referred to as Dr. President or seen a contemporary document with that usage. It was always Mr. President.
There has never been a first lady with a doctoral degree, but in the (increasingly unlikely) event of Howard Dean becoming President, I’d say it’s very likely that his wife would be referred to as Dr. Dean.
Some day they’ll have to cover this on The West Wing and then we’ll know for sure. 
If we ever get a President who is a biker, will his wife be the First Old Lady?
I’ve known several PhDs who never use the honorific “Dr.,” although they might have it on their business card (but not always). I’d bet that a President such as the OP contemplates would not be referred to as Dr. President.
None leap easily to mind at the moment, but haven’t we had some governors and senators who’ve been PhDs and MDs? How have they been addressed?
Most presidents are granted a doctorate or two, but their title is always Mr. President.
The same should carry over to a Senator, Congressman, or Justice. Mr. Senator, Mr. Congressman, or Mr. Justice is the correct form of address, at least if you’re addressing them as a government official.
Howard Dean’s already been asked and has stated that, if elected, he plans on going with precedent and being referred to as “Mr President” not “Dr President”.
Well, Abby Bartlett, the wife of the President on the West Wing, is a doctor, and at what point angrily wonders aloud when she became ‘Mrs. Bartlett’ rather than Dr. Bartlett. He’s presumably got a PhD, since he was once a (Nobel-prize-winning) economics professor, but he’s always Mr. President, not Dr. President. So now we know for sure. 
“Doctor” is an appellation (title). “President” is a rank (relative position in society).
I don’t think it’s proper to mix the two.
“Mister” is the honorific (showing respect of social superiority).
And I’d say that it’s actually very unlikely that his wife would be referred to as such, since her name is Judith Steinberg. 
Yeah, like that’s going to matter to people.
What, you mean like honorary degrees? Do those even count?
Not quite. Hillary Clinton (presumably) has a JD from Yale as she is a lawyer. A JD is technically a doctorate although its holders don’t use the honorific. If Dr. Dean is elected, hopefully his wife will be addressed as she prefers to be called: most likely, Dr. Steinberg.
Sen. Bill Frist (R-TN) is an MD and a surgeon. He is usually addressed as Senator Frist, although I have heard him referred to as Dr. Frist. I can’t recall him being referred to as “Mr. Frist”.
Robin
I read an article recently that put the point that, while doctorates have been conferred in academia for a long time now, calling people who hold them “Doctor” in conversation or using the title in address is a fairly recent convention.
Previously, that usage had been reserved to medical doctors and dentists only.
So, in President Wilson’s time, it probably wouldn’t have occurred to anyone to call him “Dr. President”. The change in usage of the term, and the candidacy of Howard Dean, are driving this conversation today.
Supposedly when Henry Kissinger became Secretary of State the press corps asked if they should address him as Mr. Secretary or Dr. Secretary.
“I don’t stand on ceremony,” he replied. “You can just call me Your Excellency and that will be fine.”
–Cliffy
Actually, calling only medical doctors “doctor” is recent. If you go back a couple hundred years, anyone with a doctoral degree was “doctor”. There’s been a lot of threads about this.
Note that in Germany, titles compound. I know several “Mr./Mrs. Doctor Professors” from Germany. (A few have even longer titles.) In the US, we usually use only the most important one. (Which for most colleges I have worked at was “Professor” but at a few it is strangely “Doctor”. It’s generally much harder to become a Professor than a Doctor.)
It is merely an oddity of English that saying “Good morning Doctor.” seems okay but “Good morning President” doesn’t. Hence we sometimes have exceptions like “Mr. President.” (Which actually sounds stuckup to me.)
Good one.
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In my book, “doctor” and “general” are roughly equivalent titles, and no president has been called “General President.”
HL Mencken, in his political reporting, regularly would refer to any politician with even an honorary degree as “Dr. So-and-so”. Then again, that’s partially the contempt of a autodidact for the educational establishment.
Ringo:
You mean like Dr. Howard Dean, former governor of Vermont?