The neoliberal ideology infects both parties, modern day democrats agree with much of Reaganomics. I'd be surprised if the right used it as a pejorative, though they may be misusing the term to apply to "new" liberalism, the social liberalism mentioned.

A quick search of "neoliberal left" brings up things like the Jacobin and Noam Chomsky criticizing the left, not something like Breirtbart.