The two situations are hard to reconcile because your moral axioms are an attempt to make a simple, coherent system starting from your moral intuitions; but your moral intuitions do not actually arise from a simple, coherent system.
In the case presented, the only differences from the toddler's are the time required to save the lives, and the psychological availability of the lives saved.
Unless your moral intuitions and/or moral axioms allow lower levels of responsibility for suffering which is easier to ignore, the "time required" is the only escape.
If you lived in a world where toddlers were perpetually falling under busses in front of you, would you be morally obligated to stay in good physical condition and pay attention to nearby toddlers so you could save more of them? If not, you should be safe from the responsibility to maximize your income and use the surplus to save lives.
In the case presented, the only differences from the toddler's are the time required to save the lives, and the psychological availability of the lives saved.
Unless your moral intuitions and/or moral axioms allow lower levels of responsibility for suffering which is easier to ignore, the "time required" is the only escape.
If you lived in a world where toddlers were perpetually falling under busses in front of you, would you be morally obligated to stay in good physical condition and pay attention to nearby toddlers so you could save more of them? If not, you should be safe from the responsibility to maximize your income and use the surplus to save lives.