Section 3 of the 20th Admendment provides that:
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. If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified; and the Congress may by law provide for the case wherein neither a President elect nor a Vice President elect shall have qualified, declaring who shall then act as President, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a President or Vice President shall have qualified.
I think a withdrawal by the President-elect would be taken as such person having "failed to qualify" but I am not sure. No such case has ever occurred, to the best of my knowledge, so there can be no case law.
The relevant law seems to be 3 USC 19 which provides that if
by reason of death, resignation, removal from office, inability, or failure to qualify, there is neither a President nor Vice President to discharge the powers and duties of the office of President
then the office goes to the Speaker of the House, and failing that to the President pro tem of the Senate. Failing that, members of the Cabinet, in a specified order, are to act as President.
In the case of a "failure to qualify" the acting President "shall act only until a President or Vice President qualifies" (See paragraph (c)(1).)