What happened in the 60s and 70s to turn a large number of "great society" voters towards Reaganomics?

To be super broad with it: Nixon, an Oil embargo, and Civil Rights.

The Great Society was predicated on the New Deal, which relied on an alliance with segregationist conservatives who resonated woth infrastructure and an industrial war economy. When it came time to extend the gains of the Great Society to non whites, they ultimately rebelled in practice.

It was also Carter who adopted the precepts of what became Neoliberalism to try and sustain the political alliance. So the oil embargo of 1979 after Iran kicked us out for doing imperialism is a huge component that crushed the party leading into Reagan.

And so Reagan followed with his conservative plans to squelch the economic futures of those guaranteed civil rights, sealing the deal by offering a solution to those threatened economically.

But finally it was Nixon before Carter who broke the trust between the American public and government. Nixon came with the prestige of being Eisenhower's VP for 8 years. His resignation was an admission of defeat that the GOP learned to never repeat at any cost, the effects we see today.

This is all brushing past the assassination of JFK that put LBJ in his position to begin with.

I don't think things like debt actually make people more conservative. I think that effect has to flow from things which actually impact peoples lives - so if the government takes on too much debt, and then cuts public services to manage that debt, which makes people feel more economically precarious, then people will statistically become more conservative. But if the debt isn't impacting people directly, then it isn't increasing conservatism. Instead, existing conservatives are predisposed to care about increasing public debt and see it (rightly or wrongly) as a threat to their way of life. But if conservatives constantly talk on the internet about how increasing debt is going to collapse the government, then more neutral people might feel threatened, and will start adopting more conservative stances.

As for what caused the shift towards Reaganomics - I'm sure we could come up with a just-so story. But I don't know if I'm the one to do it