There may come a time when it's better for the cats to be found a new home, but that would be if the OP really can't make any other savings and is still struggling.
It's actually not so easy to just get rid of the cats anyway. There's often waiting lists and the waiting times can span many months as rescue centres often just don't have the room, so it's not really a very practical, short term solution.
I knew a family that were relying on food banks and couldn't afford to feed their cat. They could only afford to feed it the cheapest dry food and even then they were having to stretch it out to make it last by only feeding it once every other day, and even then they were only giving it half what it should've had in one day.
They were of the opinion, the cat is part of the family, we can't get rid of it, but in the end they weren't being fair to the cat, as it was losing weight and wasn't happy.
As an pet owner you have to put the animal first, even if it's not what you want, and they weren't able to do that. I did eventually get them to let me call a rescue centre and I explained the severity of the situation to them and asked about them taking the cat on. I ended up ringing all such places within our county that I could get through to; not one place could do it immediately, they all had waiting lists, and the shortest list was around 3-4 months minimum. If they'd looked into it earlier, and got him onto the waiting list, it would've been better for the cat. They let their emotions get in the way of doing what was best for the cat.
I ended up paying for the cat food as I couldn't see it starve to death. I think they partly expected the cat to cope by hunting for food, but not all cats can/will hunt, and they have varying levels of success, especially when they don't have the energy spare.