Natural selection is your answer
Do different species work together to evade predators? Not that I know of, so different species working together to kill predators is even more unlikely. However, I can see how it could occur, though it is extremely unlikely.
It all starts here...
There are three fundamental evolutionary strategies animals use to survive predators: Evasion, Defense, and Offense.
Evasion is defined by an animal evolving to evade its predator. This includes, but is not necessarily limited to:
Speed and agility-Various prey animals have developed incredible speed and agility to outrun and outmaneuver predators. Examples include deer and gazelle. This strategy will not be selected for unless those below fail.
Enhanced senses-This strategy entails prey detecting predators before the predator detects them, or else detecting predators at the same time the predator senses them, and acting accordingly (read: hightailing it) to avoid being eaten. This will not work if the predator is capable of tracking down the prey, or else outrunning it upon detection.
Camouflage-If a predator cannot detect a prey animal, how will it catch and eat said prey?
However, if the predator cannot be evaded effectively, there are other options...
Defense is defined as developing greater defenses, potentially making the prey inedible to its predator. This includes:
Poison-This is exemplified by poison dart frogs. By producing or storing poison in one's body, a prey animal will cause predators to either evolve to A) not eat their now poisonous prey or B) be immune to or protected from their prey's poison.
Armor-This is exemplified by turtles and armadillos. If a prey animal develops good enough armor to protect themselves from their predator's weaponry, then the predator will not be able to kill and/or eat them.
Texture-Hedgehogs, porcupines, and so forth demonstrate this. Spikes, slime, and even the ability to bloat on demand enhance prey survival and diminish a predator's chances of eating said prey.
Offense is defined by prey evolving to attack and kill predators. This is an aggressive and risky strategy, and is probably the most unlikely of all the others. This is where you get what you're looking for.
For whatever reason, Evasion and Defense have either failed or aren't effective enough, so what happens? Well, when all else fails, the prey that survives is the prey that effectively fights back.
Also, these prey animals, no matter their species, will automatically be at a disadvantage if they fight each other rather than cats, because that entails more risk and therefore more death. In other words, I can see these animals (through natural selection and/or whatever common sense they possess) avoiding conflict with each other.
Over time, these animals will grow to tolerate each other, even choosing different food sources (or else sharing the same food sources) to eliminate chances for conflict. Then, when cats show up, what will happen? These animals have overlapping territory, yes? The cat will attack and eat whatever it can get, yes?
So, maybe, just maybe, you have a squirrel and a chipmunk, or any other pair of NYC prey animals, and a cat attacks one of them. Due to innate aggression, or perhaps due to committing to a preemptive strike, the other animal attacks the preoccupied cat and kills it. Eventually, because this enhances both species chances of survival, the cat's prey eventually evolve to cooperate to fight against their common enemy.
Is this likely? No, as I said before. But, these animals likely have different preferences. They already live alongside each other. And given the right conditions, natural selection can and will bring about this kind of situation simply because every fight won this way means another day of life, and one less cat to threaten the species. So, I hope you'll be gladdened to know it could happen!