The march toward the right was in regard to social issues, you didn't have to go all voodoo economics for that.Reagan was the product of the nation's times. It was only a matter of time before Americans became distasteful of social democracy because it helped those dirty browns and blacks.
The same could be said with Clinton. Only a "centrist" could win the presidency in '92. America had already changed by then. If Reagan didn't take the mantle at best case scenario America's march toward the right would have been a bit more gradual.
Had best Bush won in 1980, the world would've been a very different place.