I believe they mean "something with your A# on it"
As mukund points out, at this point, the only thing you have with your A# on it is your EAD. My understanding is that the A# stays with you till you apply for citizenship.
BTW, I showed them my driver\'s license and they specifically asked for my EAD. I have no idea whether they had any record of whether I had applied for an EAD or not (there were no computer terminals in sight at the front desk).