Despite the fact that Nixon surely believed himself the obvious choice for the next President of the United States, a lesser-known, but still very popular Senator from Massachusetts named John Fitzgerald Kennedy stood squarely in his way.
The resulting Presidential election of 1960 became one for the history books. The two candidates ran neck and neck throughout the campaign season, though Nixon looked as if he was going to win. Unfortunately for him, illness struck just before the two candidates were going to engage in the very first nationally televised Presidential debates, and Nixon appeared weak, pale and unshaven on television, as opposed to his young, healthy opponent.
It is unknown exactly what kind of impact this debate had on Nixon's chances in the election, but when the voting was over that November, Kennedy had won, though by only the scantest margin (and certainly not without controversy regarding possible election fraud).
Nixon had lost the election, and as a result retreated back to California and local politics.
Gubernatorial Election
Only a year after Kennedy had been sworn in as America's 36th President, Nixon was running for office again, this time engaging in an ill-advised campaign against the highly popular incumbent Governor of California, Pat Brown.
Though Nixon had never been known to desire the office of Governor, he surely was hoping to use this position as another stepping stone toward future attempts at the Presidency (and some claim that he was hoping to win so that he wouldn't be pressured into running for President against Kennedy again - a fight he would surely lose).
Regardless of his motives, Nixon lost the election - an eventuality which seemed almost inevitable. Showing signs of the kind of animosity toward the press for which he would become known during his Presidency, Nixon accused them of working and conspiring against him, and in a later press conference, Nixon formally "retired" from politics, telling the reporters present, "You won't have Nixon to kick around anymore, because, gentlemen, this is my last press conference."
Nixon appeared to have left politics entirely. He moved to New York City where he became a partner in an important law firm, though he continued to maintain a certain amount of influence in the Republican party by stumping for candidates in the 1966 congressional elections.
The Presidential Election of 1968
Kennedy had been assassinated in November of 1963 and President Johnson was elected in his own right in 1964. He declined to run again in 1968 because of ill health and a declining popularity as a result of the massively unpopular War in Vietnam, to be replaced on the ticket by Vice President Hubert Humphrey.
Nixon attempted to gain his party's nomination - taking the reigns from Barry Goldwater (the previous standard-bearer of conservatism), and opposing his primary rival to the nomination, Ronald Reagan.
Nixon was able to solidify himself with the right thanks to fervent opposition to his nomination by President Johnson himself, and Nixon was able to sew up the nomination (and Reagan dutifully threw his political weight behind him), moving on to the difficult general election, with Vice-Presidential candidate Spiro Agnew (who was even more conservative) at his side.
Nixon once again began the election with a considerable lead, and it looked at first as if the election would be a walk for him. Unfortunately for the Republican Party, President Johnson was able to push through important peace talks with the Vietnamese that fall, which provided a much-needed boost to Humphrey's campaign, closing the gap on Nixon.
Nevertheless, when election day came, Nixon was still able to eke out a narrow victory against Humphrey (at least, narrow in terms of popular vote - the electoral college victory was much more considerable).
Nixon had been elected President. Now he had to live up to his many campaign promises - chief among them: Figure out what to do about Vietnam.
For More Information:
References:
"Richard Nixon." American Presidents: An Online Reference Resource.
"Biography of Richard Nixon." The White House.