Vice president elect becomes president.
20th Amendment, Section 3
Quote:
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Section 3. If, at the time fixed for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President.
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This actually almost came up once. There was an assassination attempt on FDR after his first election but before inauguration (the mayor of Chicago was killed in the same attempt -- lesson to future assassins, don't stand on unstable chairs while shooting at the president). If it had been successful his vice president (I forget who that was) would have been sworn in on inauguration day.