If moral obligations are something humans come up with using rational means, then it makes sense to assume that one should not expect someone to do what is impossible. In this context a moral obligation is analogous to a legal requirement to behave correctly such as when crossing a street with a traffic light. There is no point in legislating behavior that is impossible to perform and there may be circumstances (such as silly decisions) that might excuse one for not behaving correctly if facing a judge and jury.
In that context humans make these moral obligations and humans fulfill them.
However, if one accepts a divine command theory, then humans do not make nor are they alone in fulfilling the moral obligations. All that is required is their obedience. Here is Michael W. Austin's description of it:
Roughly, Divine Command Theory is the view that morality is somehow dependent upon God, and that moral obligation consists in obedience to God’s commands. Divine Command Theory includes the claim that morality is ultimately based on the commands or character of God, and that the morally right action is the one that God commands or requires. The specific content of these divine commands varies according to the particular religion and the particular views of the individual divine command theorist, but all versions of the theory hold in common the claim that morality and moral obligations ultimately depend on God.
In this context something apparently impossible may be commanded, such as crossing the Red Sea or treating an enemy with justice and mercy. One can expect God, who gives the commands, will assist one in whatever is required, impossible or not. If a person makes a silly mistake and disobeys there may be ways to obtain forgiveness depending on the particular religion the disobedient person belongs to.
Austin, M. W. Divine Command Theory. Retrieved on August 21, 2019 from the Internet Encyclopedia of Philosophy at https://www.iep.utm.edu/divine-c/