Sixties politics were so different than today’s that it’s difficult to do them justice unless you lived through them.
However, here’s an extremely oversimplified version of the way they were up through 1964.
All post WWII politics centered on your stance on Communism. As with today’s attitudes on the war on terrorism, those who believed that any and all measures not only could but must be taken against the Communist menace were conservatives and those who believed that preserving American values and civil rights were as important as our safety were liberals. Isolationism was a long-standing thread in conservative politics but had mostly been discredited by WWII and was thrown out after the Korean War.
Also as with today, other, mostly domestic, political issues confused the subject. Conservatives were strongly states rights, small government advocates. Liberals mostly believed that, following the model of the New Deal and the war planning boards, not just government intervention but government planning could solve major social problems.
These cut across party lines. There was a liberal - mostly but not entirely Northeastern - wing of the Republican Party and a conservative - mostly but not entirely southern - wing of the Democratic Party. Because of these wings, mainstream politics was indeed far more bipartisan than anything dreamed possible today. They could be no playing to the “base” when the base included people diametrically opposed to any proposition.
The 60s changed everything. People get tired of hearing this, I know. For some reason they keep blaming the baby boomers, though, which is ludicrous because almost every social change, including rock music, was led by people who were born before 1946. This is so obvious that it should go without saying - 18 year olds couldn’t even vote in 1964 so no baby boomers were involved in that election - but you hear a constant drumbeat of this nonsense.
No matter. The 60s changed everything. Especially politics. Barry Goldwater’s run in 1964 was the last campaign to directly reference the Cold War as a primary issue. Johnson was going to win in any case because of the Kennedy legacy but the public decisively rejected forceful anti-Communism as the dominant Republican issue in 1964. Because of that, younger conservative groups started working toward a new coalition of American values ideas to champion.
However, the Civil Rights movement along with the Civil Rights Act of 1964 changed the social equation. The Solid South - so-called because mostly virulently racist Democrats used race as an instrument of control since Reconstruction - had been fighting Civil Rights for decades but the pictures of them doing so on television had finally brought the rest of the country to awareness of the ugliness and made a fight against them possible. (Never say anything nice about Hoover’s FBI, but he realistically had his agents ignore racial cases in the south because he knew he would get no, zero, cooperation from southern law enforcement or from his political bosses.)
Lyndon Johnson took on this fight and won. He broke the power of the southern Senators. (A few years later seniority rules in the Senate were changed to break them of their control of committees as well.) He knew what this would do to the Democratic Party - he said it would lose them the South for 25 years - and he only underestimated the reaction.
Then came Vietnam. To get it down to a sentence, let’s just say that the disillusionment of the effects of government power - brought to its logical end with Nixon and his crimes - radicalized the left, while the attacks on government and values radicalized the right.
One result was that the wings of the parties both collapsed: the liberal Republicans and the conservative Democrats no longer had constituencies because they no longer had any power and vice versa.
The other result was structural. Urban areas had long been more liberal than rural areas, but urban cores emptied out in the 50s and 60s as the suburban population exploded and the urban cores because heavily minority as a result. Suburban areas became mostly Republican in all areas of the country. But at the same time the movement toward the Sun Belt started, and the Sun Belt included all the states in which Republicans inherited, usually implicitly, the racial politics of the conservative whites. Almost overnight the Solid South was solidly Republican. Kevin Phillips, in The Emerging Republican Majority (1969) forecast this and coined the term Sun Belt.
This led to today’s political world. Aligning conservative/liberal with the two political parties is not a “Big Lie” but an exact description of the reality of the past quarter century. Each side has majorities in specific areas and reflect this in Congress, and each side has roughly 40% of the population with the other 20% deciding all Presidential elections. Bipartisanship is almost nonexistent because neither party has opposing wings to placate. The center is mostly apolitical and sways with current issues so it can be moved by appeals to special interests and negative imagery. It’s the worst political atmosphere of my lifetime and I say this having lived through Vietnam and Nixon.
Only a major cultural shift will change the political associations, but that’s GD territory, even if I don’t have the faintest idea of what this shift might be.