My name is***** and I am sorry to hear that Piccolo is not feeling well today. I know your question is when should you take him to the emergency room and I don't have a straight forward answer for you.
First I would wonder what is causing Piccolo to have vomiting and diarrhea yesterday and not want his food today? Does he have intestinal disease such as inflammatory bowel disease or lymphoma? Does he have some other metabolic disease such as kidney failure, diabetes or liver failure? Does he have a disease that is easily treatable if you take him in right away vs waiting until tomorrow to see your regular vet? Does he have a fever?
Typically, when talking about cats eating or not, I say that if they are eating at least once every 24 hours, that is okay. So on the surface, you could, in theory, wait until tomorrow to see your regular vet, but again, I am still worried about what is making him so lethargic.
I am really sorry, but I cannot accept a phone call due to restrictions on my license. I can continue this conversation until all of your questions are answered, though.
Best regards, ***** ***** this answer helps you.
Feel free to contact me if you have any more questions.
Kansas State University,
College of Veterinary Medicine Class of 2001