Google voice is your friend here. I actually made up business cards to give to car salesmen with my google voice number, a po box number, and an email address i can check but never use. I have my real name on it, because they ask for your drivers license if you take a test drive.
Saves me from having to remember my "fake" information on the spot, I just whip out a card and give it to them. Any time someone asks for a phone number from me and I don't want them to call me, I cheerfully give out my Google Voice number and never answer the calls. They forward to me, so I know I was called, but I "reject" them to voice mail and if they leave a message I get an email and a text message with an often-amusing voice to text transcription of what they said (some are hilarious). So I can accurately report the date and time of the contacts they tried to make without having to talk to them.
When they become a nuisance I answer one and tell them I decided to keep my old car, or bought somewhere else (depending on how much they pissed me off when I tried to end the interaction) and tell them to stop calling. Ironically the one that called me the most after I left is the one that refused to budge on price (quoted me sticker price and not a dime less) when I was in the showroom. Within a day the offer was $500 under invoice. Rudest sales manager I've ever met at that place; I'd take the bus before I would have bought a car from him.
I also use bgriffin's tactic of snagging a card when the salesman left the room. Slip it in my pocket and get ready to turn him down and make my escape as quickly as possible. It avoids encouraging him falsely by asking for one.
The first one will be rough; they'll get easier as you do more of them. Just don't shop a car you really would like to buy unless you're sure you can't qualify for the loan.
You might be tempted because those offers do get sweet at times. I was on one shop where I liked the sales manager's approach so much I really wished I'd been in the market for that Nissan Sentra. He offered me a great deal out the gate, offered to deliver the car to my town (90 miles away), and was respectful of me and accepted my rejection. I find the best ones are the 50+ year old ones. They've learned that high pressure drives people away. The gung-ho 25 year olds are the worst. They usually quit before they learn what the 50 year old knows.
Time to build a bigger bridge.