You have some tough choices to make when you find stray cats living in the attic. The family is not your responsibility. It was never your pet, after all. At the same time, however, that furry little family could very well tug on your heartstrings, encouraging you to add a few more to your household.
Whatever decision you make, make it wisely. Do not become another irresponsible pet owner who causes these stray cat situations in the first place.
In order to help you answer your difficult questions, ask yourself a few more:
Do you know whether or not the cat is a stray? Could it just be a little lost family pet? Is it wearing a collar? If it isn’t, could it be a feral cat? There’s a very big difference between feral cats and stray cats, the laster being somewhat adapted to human interaction and the former not being comfortable with humans at all. There's a chance you could win over the animal with food, particularly if food has been scarce for the new family. At the same time, however, there's a chance that you have NO chance of winning the mother around. She will be fiercely protective of her young, and that's where you could find yourself worse off.
If the cat has a collar, check it out. If it won't let you get close enough, call in the professionals. Trapping a mother with her babies is going to be hard work. You would need to wait until the mother has left to find food, capture the babies (wearing thick and protective rubber gloves), place them as bait inside the trap, and then wait for the mother to try and retrieve them. She will then be caught in the trap, and you can take the cat to the vet.
The professionals can capture the mother and then grab her young for you, if you do not have the necessary or appropriate safety equipment. They can also take the cat to the vet to get it checked over.
If the cat has an owner, the animal can be safely returned. If it does not, or the cat isn’t registered, the cat will be checked over for diseases and given the appropriate vaccinations. It will also be neutered to ensure no further stray or feral cats. If the cat is very sick, however, or shows serious behavioral problems that cannot be resolved, there is no other choice but to put the animal down. Sadly, this happens more often than not, and it all starts with a cat that is left out in the cold, for one reason or another.