I know he can only be elected to two terms. But what if he was elected vice president and the president died 30 days into his term. The vice president of course would take the office.
Will he still be able to run two more times?
Ten years.
And in the scenario in the OP, the VP could run once for reelection, but no more (since a second reelection would mean his term was more than ten years).
If he serves more than half a term, it counts as a term, otherwise it’s bonus time. I’m not sure if Johnny L.A. is right or if it’s one day short of 10 years.
You are so unbelievably wrong it is unfathomable. I am pretty sure it is ten years minus 1 day. 
Actually, the 22nd Amendment below could cause problems if the president was assaisnated exactly in the middle of the year. Is it a matter of days, seconds that define the middle of the year? Do leap days play a role.
Amendment XXII
(The proposed amendment was sent to the states Mar. 21, 1947, by the Eightieth Congress. It was ratified Feb. 27, 1951.)
Section 1
[Limit to number of terms a president may serve.]
No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once. But this article shall not apply to any person holding the office of President when this article was proposed by the Congress, and shall not prevent any person who may be holding the office of President, or acting as President, during the term within which this article becomes operative from holding the office of President or acting as President during the remainder of such term.
What if he runs as a congressman and becomes speaker of the house and the POTUS and VPOTUS die before the inaugaration?
With respect to answering the OP, two terms or eight years, providing he is constitutionally eligible to be POTUS or VPOTUS.
Again, it is clear.
The first sentence of the 22ns Amendment says:
“No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President”
We have had plenty of threads about slipping an ex-pres like Clinton in through some convoluted plot but the consensus is that it isn’t allowed under any circumstances.
I’m ashamed I don’t know this, but how did FDR get elected four times? Was the law not in effect, or did they put in on hiatus during WWII?
Shagnasty answered your question.
The 22d Amendment wasn’t on the books until 1951, near the end of Harry Truman’s term. As noted in the text, Truman could have kept running forever if he wanted to; he was not affected by the Amendment. Eisenhower, however, was term-limited out.
–Cliffy
Ten years: no “minus one day.”
The Amendment specifies that “no person who has held the office of President, or acted as President, for more than two years” so a person who was president for up to two years is not disqualified.
We can still argue whether the two years is effective at midnight between January 19 and January 20 or whether it is effective at noon on January 20 (and, if January 20 closing the partial term falls on a Sunday with the inauguration moving to Monday, January 21, is the acting president then disqualified from a second election if s/he took office on January 20), but it is not based on “minus one day.” 
That’s the part I was talking about. Where exactly do you define the change from the first two years to the second? The minus one day was to play it safe. If the distinction is finer than that, we have to know whether it is down to the nearest hour, minute, picosecond what?
If the Constitution and Federal Law was a computer program we would consider it quite buggy and vulnerable to unexpected data.
I’m having fears that we’re going back to the debates around the time of the 2000 election if Clinton could come back as president if he were named VP.
Man were there a lot of threads like that.
Too bad this thread isn’t in GD. One could have a field day with a comment like that.
Which is why the system is designed with a Supreme Court, whose job it is to de-bug such items.
I think it could be more than 10 years, but it’s highly unlikely. A person could serve multiple times up to 2 years of the balance of other persons’ terms of office. Of course, in practice that’s highly unlikely: no person who has served as President of the US has ever run subsequently for the office of Vice-President, but (at least in theory) they could for an unlimited number of times.
I don’t understand how that’s a valid conclusion from the text quoted here. I don’t want to rehash the debate (I remember those threads, too), but how does “No person shall be elected to the office of the President” effect who may be elected to the office of VP and then later assume the Presidency?
The argument comes from Amendment XII, which states:
A Vice-President who cannot act as President therefore cannot be named Vice-President in the first place.
Never been tested, obviously. But this would seem to preclude Clinton and Bush from running as Vice-President or being appointed to the post in the future. That’s the argument, at any rate, not to rehash it either.