If Donald Trump's reported statement to CNN's Anderson Cooper that "President Obama's birth certificate cannot be found or may not exist turns out to be correct, and if subsequently, upon investigation, President Obama's election in 2008 is decided to have been illegitimate due to his disbarment from running for the office of president under the Constitution then his removal from office may be undertaken.
The current vice-president Joe Biden would have no apparent legitimate hold on office as he would not have been elected in 2008 if his running made had no right to seek the Electoral College majority. Further he would have, surely, no moral right to the office.
The 20th amendment ot the Constitution gives a clear legitimacy to, where a presidential and vice-presidential canddiate, having failed to be qualified, disbarring them from those offices. Congress can clearly, at that point, choose the legitimate office holders.That choice would surely have to be the two persons who received the highest number of legitimately received electoral and popular votes-John McCain and Sarah Palin who would be sworn in immediately upon selection by Congress under the Constitution.
The 20th amendment to the Constitution, Section3.:
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. 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.