I did a search and found this on Purina's website:
I was curious to know if a toxic spider - such as a black widow or any such kind - ever bit my cat, would my cat get sick and die, or just get really sick? If he did get bitten, would we be able to tell? Are there any positive signs he got bitten by a spider?
There are no signs that a cat has been bitten by a spider, per se. There are signs, however, that a cat has been bitten by some kind of insect. The main sign is a large swelling, usually on the muzzle or on the foot, with no particular evidence of pain. On rare occasion, hives will appear on the skin. The swelling or hives represent an allergic reaction that is not life-threatening. The swelling usually goes away within 48 hours. Spider bites can be different, however. They can be much worse in that the swelling can last for weeks, and the tissue around the site where the cat was bitten can die and slough off, leaving a large skin wound that requires major veterinary care.
Only two types of spiders are capable of causing severe injury to your cat: the female black widow and the brown recluse. The black widow is a shiny black spider with a red hourglass-shaped spot on its underside, about 3/4 of an inch in length. It is found all over the Unites States. Signs of a black widow spider bite are severe pain at the site of the bite, muscle spasms, drooling, seizures, difficulty breathing, and paralysis. The paralysis may happen pretty soon after the bite and may be severe. The cat must be examined by a veterinarian immediately. There is a good chance that the cat will die from this bite.
The brown recluse is a brown spider, a half-inch in length, with long legs and a dark brown fiddle-shaped mark on its back. It is found mainly in the southern United States. At first, there is little pain or swelling associated with the bite of a brown recluse spider. After a few hours, a blister will form. After one or two weeks, an ulcerated area will develop, and the cat may develop a fever and joint pain. The cat needs to be examined when the ulcerated area forms, and the damaged tissue will have to be surgically removed, most likely, so that the surrounding skin does not also be come affected. It may take weeks or months for the entire area to heal properly.
If you catch an insect bite early, or if your cat receives multiple bites or stings from bees, wasps, or hornets, or if your cat begins showing signs of anaphylaxis (allergic reaction; vomiting, diarrhea, difficulty breathing, shock, collapse), emergency veterinary care is needed.