It's hard to trace those causal lines, but here's one data point: Dennett's ideas have spread rather widely, and Dennett is an enthusiastic Quinean naturalist, and indeed was a student of Quine. Here's Dennett:

...Quine’s book, 'From a Logical Point of View', which I read in despair in the math library late at night that freshman year, because I was taking a very difficult course in logic. And the next morning I’d read the whole book and I decided to transfer to Harvard to work with him.

Also: Stich, who might be called the 'founder' of experimental philosophy, was also an enthusiastic student of Quine's. And experimental philosophy is the kind of philosophy getting all the major press in the last 10 years, it seems to me.