That's movement amongst the politicians, as reflected in Congressional votes... it isn't the movement of the public, and it isn't popularity of any particular ideas. Note that the graph goes back to 1963, so Reagan is somewhere just above the midpoint, and the overlap basically disappears around 1990. That's Clinton-era... but no, it wasn't because of Clinton, it's only time-correlated. The movement began much earlier, and the vitriol against Clinton was more likely because of the divergence than the other way 'round. And no wonder Congress has been so disfunctional in recent memory... but it's not the Democratic politicians that changed.
That helps to explain why, for example, even though the ACA is gaining acceptance in popular polls, and specific provisions of it (most notably coverage for pre-existing conditions) have always been popular with the public, the politicians in the GOP are still hell-bent on "repeal and replace," or at least just "repeal."
The same tweet has a graph showing more recent popular movement:
Here both sides are diverging, bulging away from each other and pulling the white median lines apart... but there's still overlap. There's still hope of working together in the general public. And the movement is "only" a bit over a decade old at most. I'd be interested to see a year-by-year breakdown; I bet it's even more recent than that---I bet it's Obama and Tea Party old. But that data isn't in the graph.