The invoice information is only peripherally useful. Go to
Cars Direct. They will give you a figure that you can actually
buy the car for, which should be the absolute most that you should pay the dealer. If the dealer won't beat the price then you can just buy from Cars Direct.
Note: Cars Direct makes a profit, of course, so the dealer should be able to beat it by a couple of hundred dollars at least. Also, while I've usually found Cars Direct prices to be close to the minimum realistic price (plus their profit), they aren't always but even then they are at least good for setting an upper bound.