Regarding your last "if they still won't budge" and going to a different dealership, that part can be your most powerful weapon: always be willing to walk. Walking away is an important ingredient in any kind of negotiation, not just car sales. Many times I've had the salesman call me later the same day with a better price a lot closer to what I'm willing to pay, especially if you visited the dealership at the end of the month.
>> "especially if you visited the dealership at the end of the month."
surprised no one else has mentioned that tidbit. If the dealership closes out metrics at month-end, they'll be in a deal making frame of mind at that point. ++ if you can snag a salesperson that hasn't been doing well.