I've had luck with this technique as well. I generally make a deadline a few days out though which gives me a little time to work the phone without being overwhelmed. Some dealers do NOT want to deal this way ("You need to come here to get the best price"), but enough do deal over the phone to make it easy enough.

Now, the best way to save money on cars is to play the meta-game! Looking for a car which is not as popular or rare will give you much more bargaining power. End of model year, end of platform, etc are other good deals. Also having many dealers to compete works better than manufactures with less dealers (I have 10+ Ford dealers nearby, but only 1-2 VW dealers for example)