Twenty-second Amendment to the United States Constitution
Some argue that the 22nd Amendment and 12th Amendment bar any two-term president from later serving as vice president as well as from succeeding to the presidency from any point in the presidential line of succession. Others contend that the original intent of the 12th Amendment concerns qualification for "service" (age, residence, and citizenship), while the 22nd Amendment, concerns qualifications for "election", and thus (strictly applying the text) a former two-term president is still eligible to "serve" as vice president (neither amendment restricts the number of times an individual can be elected to the vice presidency), and then succeed to the presidency to serve out the balance of the term (though prohibited from running for election to an additional term).
United States House of Representatives
Under the Twelfth Amendment, the House has the power to elect the President if no presidential candidate receives a majority of votes in the Electoral College. The Twelfth Amendment requires the House to choose from the three candidates with the highest numbers of electoral votes. The Constitution provides that "the votes shall be taken by states, the representation from each state having one vote." It is rare for no presidential candidate to receive a majority of electoral votes. In the history of the United States, the House has only had to choose a President twice. In 1800, which was before the adoption of the Twelfth Amendment, it elected Thomas Jefferson over Aaron Burr. In 1824, it elected John Quincy Adams over Andrew Jackson and William H. Crawford. (If no vice-presidential candidate receives a majority of the electoral votes, the Senate elects the Vice President from the two candidates with the highest numbers of electoral votes.)