The one thing I have heard is Clinton shifted the Dems to the right on trade policy and economic globalism and Free Trade. NAFTA and TPP remain unpopular with the far left (also unpopular with the far right).
That's more a centrist policy, the edges of both parties oppose such things.
Also, it barely fits your timeline, and this became Dem policy in the mid/early 1990's - but remains a contentious issue.
I think Clinton also shifted the window right on some other economic issues, including some arcane regulatory issues that affect banks and stock trading and the way large businesses can structure their assets. Stuff I don't personally understand, but the far left seems to think it contributed towards the consolidation of wealth and power into a smaller group of people and large companies.