Explain the evolution of Cold War liberalism between 1945 and 1968, that is from the presidency of Harry S. Truman through John F. Kennedy and to Lyndon Baines Johnson. Why did Jimmy Carter eschew the label during the 1976 election?

American liberalism post-World War II was heavily influenced by the economic policies put into place by the liberal presidential administration of Franklin D. Roosevelt. Roosevelt, of course, was first elected president while the country was in the depths of the Great Depression, with astronomically high unemployment and a financial system in total disarray. Some of the major New Deal programs that helped to lift the nation out of the Depression, such as the Civilian Conservation Corps, Civil Works Administration, and the Public Works Administration, would wither away or be reestablished in later years under different names and with modified missions. Others, however, survived the war years and continued to exist. Among this latter category are Federal Housing Administration, the Social Security Administration, the Farm Credit Administration, and the Tennessee Valley Authority. These agencies survived because a strong strain within American liberalism viewed such organizations as essential to the welfare of the lower and middle classes and, consequently, became increasingly synonymous with liberalism in the years following the end of World War II.
While liberalism in the United States was increasingly defined by its commitment to social welfare and jobs programs like those from the New Deal, the country had emerged from the war very much rejuvenated economically, politically and spiritually. The 1950s, then, became a period of relative prosperity, with the concerns of most families focused more on external threats (i.e., the growing power of the Soviet Union) and on the perceived threat of communism at home--a fear that manifested itself in the Red Scare and the blacklists that prevented some in the entertainment industry from being able to ply their trade. Foreign policy considerations were largely determinative of the policies advanced by both major political parties during this period, with the Democratic Party split between those who shared the concerns of more conservative areas within the country about the spread of communism and those who sought to ameliorate the threat from the Soviet Union and its allies through advancement of the Truman-era policy of containing the spread of communism and of Soviet encroachment by bolstering alliance networks around the globe while supporting military activities intended to confront or weaken communist and/or pro-U.S.S.R. activities in what was being called the Third World.
American liberalism did not really begin to come into its own until the election of John F. Kennedy (a relatively moderate and sometimes conservative United States senator). While conservatives wholeheartedly supported the candidacy of Republican Vice President Richard Nixon, liberals lined up behind this young, attractive and wealthy senator from Massachusetts whose entertainment industry supporters helped popularize his candidacy. To many, Kennedy represented a major break from the Eisenhower-era politics and staid social customs that had dominated politics for many years. While Kennedy's record as president--a tenure cut tragically short by his assassination three years into his first term--was decidedly mixed (e.g., as a senator, Kennedy had been a vocal proponent of containing communist aggression in Southeast Asia, a policy that manifested itself in his support for dispatching military advisors to Vietnam, and, as president, his record on civil rights was not as positive as it should have been, for various reasons), his was considered a vibrant presidency that better represented the social and cultural transformations taking place across much of the country.
While liberalism under Kennedy took a step forward in terms of the young president's rhetoric about public service ("ask not what your country can for you, ask what you can do for your country"), including his establishment of the Peace Corps, it was his successor who moved the legislative agenda to advance the cause of liberalism forward. Lyndon Johnson, Kennedy's vice president who succeeded the murdered president, was an enormously complicated and very skilled politician. Johnson's keynote program was aggregately called "the Great Society." Just as Roosevelt's New Deal referenced a panoply of economic programs intended to spur economic growth and reduce unemployment, the Great Society was a term used to describe a long list of social welfare and civil rights programs that fundamentally remade American society and the public's perception of the government's proper role in society. The Civil Rights Act of 1964, the War on Poverty, the establishment of the Medicare and Medicaid programs, passage of the National School Lunch Act, the Food Stamp Act, and the Head Start Program were all implemented as part of the Great Society program that Johnson hoped would mark his legacy. 
Unfortunately for Lyndon Johnson, his Great Society was overshadowed by the growing American commitment in Vietnam, as well as neighboring Laos. As that commitment grew, and as Johnson authorized the deployment to Southeast Asia of hundreds of thousands of American soldiers in what was fast becoming an enormously controversial military effort, public consternation, overwhelmingly among liberals, regarding that expanding military effort detracted the president's attention and energy away from the domestic social welfare programs of which he was most proud, and he would decide against running for reelection, forever bitter about his inability to advance his social welfare agenda further than he did.
Johnson's decision not to run for reelection created an enormous vacuum among Democrats, into which slid populist liberal politician Eugene McCarthy, the late President Kennedy's younger brother (and former attorney general) Robert Kennedy, and Johnson's vice president, Hubert Humphrey. While the latter candidate would eventually win the nomination, due, in no small part, to Robert Kennedy's assassination, the Democratic Party was almost torn apart in the process, most notably in the riots that occurred around the Democratic National Convention in Chicago in 1968. Humphrey, of course, would lose in the general election to Richard Nixon, and the rest, as they say, is history.
American liberalism underwent a fundamental transformation between 1945 and 1968, with a marked turn to the political left. Jimmy Carter's election occurred within the context of the American public's exhaustion from the final years of the Vietnam War and from the Nixon Administration's fall from power following the revelations that would become known as "Watergate." Carter's election reflected a desire among many Americans for a break from the status quo--which Nixon's successor, Gerald Ford, seemed to personify. Carter was no conservative, but he was hesitant to allow himself to be categorized as a liberal because of the crowded field in which he was running for office. There were, at one time, as many as 17 Democrats seeking the nomination, including liberal stalwarts like Morris Udall and Sargent Shriver, as well as conservative Democratic Senator Henry Jackson. Carter's campaign was predicated upon his ability to present himself as an outsider. He wanted to distinguish himself from the pack, and he succeeded. Unfortunately for him, the Cold War would overwhelm his administration, and social policies were given less priority and attention than he would have liked.
https://www.politico.com/magazine/story/2015/09/2016-election-1976-democratic-primary-213125