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).
Twentieth Amendment to the United States Constitution
Section 2 moves the yearly start date of congressional sessions from the first Monday in December, as mandated by Article I, Section 4, Clause 2, to noon on January 3 of the same year. This change eliminated the extended lame duck congressional sessions. As a result of this change, if the Electoral College vote has not resulted in the election of either a president or vice president, the incoming Congress, as opposed to the outgoing one, would have to do so, following the process articulated in the Twelfth Amendment.