You can do this only if you have a particular car + all configurations in mind and won't budge. Dealers know this "trick" and what they do when you tell them you only have $10k is that they sell you an $8k car for $10k. That's how it works. So be careful. Pick the car first then say how much you only have.
Another problem I found is that if you want a particular car model and you don't live a in a large metropolitan area you might only have 3 or 4 places to choose from. They know it too. You walk away from all 3 or 4 places now you have to drive 100 miles to another city perhaps.
Another nasty thing, car salesmen in an area, know each other. A lot of dealerships are revolving doors and salesmen just rotate from one to another. When you go to one and tell them the other dealership's price, they say "Oh Joe, he is so silly, he used to work here, we can do better, we can give you $100 less".
In the end of the day you also don't know how pressed they are to sell that car. If there is a line at the door waiting to pay $1000 more for it. You'll just have to walk away without a car.
One more thing. Car options. A lot dealerships will put "crap" on your car. Nitrogen filled tires. Fancy decals. Anti-fairy-dust coatings. All that cost maybe $50 dollars or so but tell you all those things cost $1000 more, but they are "giving them away" for $500, and they put them standard on every car. So the price they quoted you through email, doesn't exist because all cars have these extra features. So don't fall into this one.