Twenty-second Amendment to the United States Constitution
As worded, the primary focus of the 22nd Amendment is on limiting individuals twice elected to the presidency from being elected again. Due to this, several issues could be raised regarding the amendment's meaning and application, especially in relation to the 12th Amendment, ratified in 1804, which states, "But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States". While it is clear that under the 12th Amendment the original constitutional qualifications of age, citizenship, and residency apply to both the president and vice president, it is unclear whether someone who is ineligible to be elected president could be elected vice president. Because of this apparent ambiguity, there may be a loophole in the 22nd Amendment whereby a two-term former-president could be elected vice president and then succeed to the presidency as a result of the incumbent's death, resignation, or removal from office (or even succeed to the presidency from some other stated office in the presidential line of succession).
Lyndon B. Johnson
As he had served less than 24 months of President Kennedy's term, Johnson was constitutionally permitted to run for a second full term in the 1968 presidential election under the provisions of the 22nd Amendment.
Initially, no prominent Democratic candidate was prepared to run against a sitting president of the Democratic Party. Only Senator Eugene McCarthy of Minnesota challenged Johnson as an anti-war candidate in the New Hampshire primary, hoping to pressure the Democrats to oppose the Vietnam War. On March 12, McCarthy won 42 percent of the primary vote to Johnson's 49 percent, an amazingly strong showing for such a challenger. Four days later, Senator Robert F. Kennedy of New York entered the race. Internal polling by Johnson's campaign in Wisconsin, the next state to hold a primary election, showed the President trailing badly. Johnson did not leave the White House to campaign.