Had a similar thing happen at Kohl's last year when I thought I was signing up at the register for a rewards points program number. When the fast-talking clerk got to my social security #, I realized what was happening and called it off. I don't keep the SS card in my wallet, by the way.
There's rarely a good reason to give your date of birth either, except at places like the doctor's office where every medical person you meet past the front desk keeps asking, I guess to prevent insurance fraud or make sure they don't replace the wrong person's hip.;)