The 60's were the first wave. Yes, they moved right since then, but starting with the people who suffered from Bush Derangement Syndrome, the push has been to become more lefty.
The Pew Research Center data bears that out.
The Democrats are further to the far left today than the Republicans are to the far right, period...
I guess it really depends on how you define "left" and "right."
In my view, actual election results would be a stronger indicator than whatever opinion polls are published by Pew. All we need to do is look at who each party selected as their candidates in the last election. The Democrats clearly rejected the more left-wing Sanders in favor of a pro-corporate, pro-Wall Street capitalist and globalist. That, just by itself, proves that they can't be all that far-left.
And the Republicans...well, look who they picked.