That was kind of my plan too, but they still managed to waste my time. It's what they do. If I wasn't sitting with my DD and DW, I might have walked, but they know that you must have some reluctance to walking, even if it's only because you'd need to drive X miles to another stealership.
My plan included having internet quotes in hand that were at a level I was willing to pay. But they played games. They write up the deal and it doesn't come back with the right price. Do you simply get up and walk out, or do you say "That's $1,800 too high, what happened to the internet deal?" and let them sharpen their pencil? I did the latter. Then I figured if the other dealer could get below MSRP by 10%, why can't you do that too, so once I had the internet offer, I made an offer that was a bit more than 10% off MSRP and ended up getting that.
Each time they pulled the "I don't know if they'll approve this, I'll go to bat for you...", DD and I giggled and reenacted the scene from "Fargo" where the salesman goes into the manager's office and talks about sports while the customer waits, lol!
https://youtu.be/E5gwc4UizUc?t=15