Your cat's problem depends on what kind of anesthesia your cat for her surgery. Not all feline spays are performed using an endotracheal tube. If an endotracheal tube was used than the information that Ireneo posted is valid.
Aspiration pneumonia can occur if your cat had not been completely fasted prior to surgery and NO endotracheal tube was used. However it can occur even with an endotracheal tube under some rare circumstances.
Regardless of the cause, a chest X-Ray would help with the diagnosis, and an anti-inflammatory, bronchodilator, appetite stimulant and other medications, in addition to anti-biotics may be necessary. It is imperative that your cat eat to prevent hepatic lipidosis (fatty liver disease).
Just wondering how your cat is feeling today. When an animal or human has a tube inserted during surgery it's quite common to have some irritation in the throat for awhile. I remember coughing for a couple days after my surgery this year. Perhaps it's just a matter of a sore throat from the tube.
Aspiration pneumonia is caused by the animal getting something (fluid or food for example) into the lungs. I'm sure your cat was off food and water before the surgery so it's not likely it vomited up debris during the procedure. Certainly if you have questions or your cat appears to have a fever and is declining, you should call your vet again. Don't wait too long.