I used the program in March and came in $800 below invoice on a Mazda. I also checked Edmunds and the price quoted through AmEx was actually quite good, so I went with it. Three dealers phoned me and I actually mentioned to one of them (my local dealer) that one of their competitors (72 miles away) had a lower price, so they matched it. It was a very painless process.
One of my colleagues is after a Prius. He has been negotiating with dealers for several weeks and I gave him the AmEx link on Monday. AmEx was $1,200 below what he was able to negotiate on his own.
I've tried Costco and others, but AmEx seemed to work the west for me (with minimal hassles).