Just made my ressies last night for December. She took my credit card number and told me that I had two options:
1. I could pay the total now while on the phone, or
2. I had to pay the total 21 days in advance of our dinner date and my cc would just "hold" the reservation.
She said I would get a confirmation letter in the mail and it would let me know when the total had to be paid in full (21 days before). If I did not pay it by that date, the ressie would cancel.
So, no, you can not pay in cash.