I suspect the social intuition of when we consider someone obligated has at least a little to do with the level of personal sacrifice required.
As in, you are almost always obligated to be good if it the personal cost to you is nothing,and you are almost never obligated to be good if it costs you a great deal. (Which is why you are obligated to save a drowning child but you are a hero if you save the same child from a dangerous burning building.)
If Singer says we’re “obligated” to be effective altruists, he’s trying to transfer the social norm we have for being obligated to save drowning children because the personal cost is very slight, over to being obligated to, say, buy mosquito nets, because the personal cost is very slight.
(personal morality, divorced from social ideas of what is an obligation, of course, might widely differ)
That’s also combined with whether the person is culpable. (You’re obligated to clean up your mess, but you’re extra good if you clean up someone elses.)