I tried and couldn't get any dealer to sell me any car for anywhere near "invoice". I told them all the price I was willing to pay and they'd say "sorry" and walk me to the door. Never a call back once from any of them.
In the OKC metro area, I know you can deal at invoice or below. Not everywhere, but some definitely will.
One key point you may have missed - don't deal with the sales force that meets you in the lot. Call the dealership first, ask to speak to the Sales Mgr and get his/her name. Then when you are mugged in the lot as you arrive, just tell them that you're here to talk to "Sam".
When there's no sales commission involved, there's simply more room to come down. That Sales Mgr is (or should be) interested in holdback and units moved. Also, be aware that the longer the car sits on the lot, the more the dealer's holdback degrades...that's their incentive for quick sale. If you're ordering, they can expect/predict full holdback.
If you're buying off the lot, going in the last week of the month can help, too. Next month, the holdback award to the dealer will be lower.
And for those who don't know,
never go in without a list of invoice prices for the models/options you are interested in. Without that, you're a sitting duck...and that information is just too easy to get. A little homework can save thousands.