An interesting followup to your example of an oiled bird deserving 3 minutes of care that came to mind:

Let's assume that there are 150 million suffering people right now, which is a completely wrong random number but a somewhat reasonable order-of-magnitude assumption. A quick calculation estimates that if I dedicate every single waking moment of my remaining life to caring about them and fixing the situation, then I've got a total of about 15 million care-minutes.

According to even the best possible care-o-meter that I could have, all the problems in the world cannot be totally worth more than 15 million care-minutes - simply because there aren't any more of them to allocate. And in a fair allocation, the average suffering person 'deserves' 0.1 care-minutes of my time, assuming that I don't leave anything at all for the oiled birds. This is a very different meaning of 'deserve' than the one used in the post - but I'm afraid that this is the more meaningful one.