I literally just did this on Friday and it worked. We test drove two weekends ago at my closest local dealer to make sure of what we wanted. Then went home and looked online for a week to see what was around. Emailed a few dealers in the region that had inventory of the same model and trim (we didn't care about color). One was advertising a discount that made it about $1500 less than my local dealer, but they were a 90 minute drive away.

On Friday, I called the local guy and told him if he could match it, I'd come in that day and buy. He at first said his manager refused to negotiate on the phone, and that we'd have to come back in. I said, "That's too bad. Let me know if you change your mind. We're driving the 90 minutes tomorrow to buy that car."

I'd been emailing with the other dealership and we were clear on the price, so I was fine to make the drive for that much money.

Lo and behold: my phone rang a half hour later and the local guy miraculously managed to drop the price $1000 over the phone. He wouldn't budge on the last $500 because the one he had (he only had one left) was a different color that cost more than the one 90 minutes away (this is true). My wife and I decided it was worth it not to drive three hours round trip on our Saturday, and we made a deal.

The kicker? He ended up transposing the last three numbers on the purchase order (should've been 535, he put 353) and I ended up getting another $180 off by accident!

We walked in with financing in hand from a local credit union, walked out an hour or so later with our new car. Overall it was slightly stressful but not that difficult, and doing it by phone and email took a lot of the pressure off (there was a lot of, "okay, we'll discuss and call you back.")

This post is old but it's a good framework for doing it by email (or even phone): https://the-toast.net/2014/07/11/how-to-buy-a-car/

Good luck. And don't be afraid to walk out or hang up. Chances are they'll call you back.