What would be interesting would be to see the same data plotted going back several decades prior to 1964. I would not be surprised to discover that the views have risen and fallen on numerous occasions and using 1964 as a starting point simply gives an erroneous impression that the positive views used to be typical, when using that date might have simply been a high water mark. (Note that the line from 1958 to 1964 is rising: prior to 1958, the views could have been either higher or much lower.)
In 1964: we had a decent economy; were beginning to see the results of the Space Race with the implentation of Telstar 2 and other satellites along with the close of the Mercury program and high hope for the Gemini program; we were only a year and a half away from the Cuban Missile Crisis that we perceived we had “won”; JFK had just been assassinated, bringing a sense of solidarity to the country; the Civil Rights Bill of 1964 and LBJ’s announcement of a “War on Pverty” had given many people, (clearly not all), the sense that the government would address injustices in society; efforts to “fight communism” were in the news, notably very minor escalations in Vietnam followed by the Gulf of Tonkin incident in which the U.S. flexed its military muscle, (generally an action that increases support for a government).
Following 1964, there was increasing division over the Vietnam War, disillusion that the government was neither effective nor correct in its handling of racial issues and poverty programs. Then news of Nixon’s behavior, (highlighted by, but not limited to the Watergate scandal), the withdrawal from Vietnam with the later fall of South Vietnam, the (perceived) inability of Nixon, Ford, or Carter to deal effectively with inflation and then stagflation, the rise of the conspiracy movement regarding JFK’s assassination that reinforced the notions of corruption or incompetence in government, (reflected in the “moon landing hoax” CTs, etc.). The nadir, of course, coincided with the Iranian takeover of the U.S. embassy, the failure of the rescue mission, and a general perception that Carter was not capable of being an effective executive.
Without genuine numbers for earlier years, it is not possible to know whether 1964 was an extradordinary anomaly, (although I would guess that from 1945 through 1964, the numbers probably trended higher). What would the numbers have been for 1931?
At a guess, I would think that the blatant deceptions in multiple venues uncovered during the Nixon presidency probably set a tone of distrust that has continued through to this day, but a general rise and fall as the country faces various conflicts is probable, regardless where a median line would plot.