This really depends on how hungry the cat is. Feral cats commonly kill mammals larger than NYC rats, although they prefer smaller game. In general, you can expect a feline to be able to kill prey over twice it's body weight. In many habitats felines are the apex predator, and even feral cats are apex predators of some habitats.

The biggest issue is that NYC rats, the non-native species that have evolved in urban environments, have evolved with cats as a predator for a long period of time and are better than native birds/small mammals at evading cats. Cats eat the native population at a higher rate, which means the invasive and hated 'NYC rats' have less competition from native populations.

Imagine how many more rats would get to that size if cats didn't get them when they were smaller. Or if they could breed in spaces currently occupied by cats.

We gonna need bigger cats