I have a hard time beliving that every cat in amarica was hunted to extinction.
There aer over 81 million in households alone, without counting all the strays, and cats in the animal shelters. And ofcourse, cats do breed, and can live in prides. ((hee hee. Kitty pride))
Theres an amazingly high chance that cats would still exist in the wasteland. While they may not be common, chances are if you found 1 cat, youd find a rather large group of them. Probabaly 30+ per "group". They could hunt together and easly take down rats, birds, or humans.
Cant probably wouldent be hunted to extinction, but there would only be a few million across the US. And they would try to avoid humans or other large creatures.
Rare? Probably. Extinct? Definitly not.