1. If there is no God then there are no moral duties.Of course, both premises need to be defended, but I don't think it's hard to defend 1. (though 1. is precisely the assertion Sam Harris wishes to deny in his book The Moral Landscape) and denying 2. leads the denier ineluctably to moral nihilism. So, it seems that if 1. can be defended one either has to believe there is a God or be a nihilist.
2. There are moral duties.
3. Therefore there is a God.
Few non-believers are prepared to embrace moral nihilism so they're in an awkward position. Unwilling to accept belief in God they're also unwilling to accept the logical conclusion of their atheism.
This appears to be the predicament in which Princeton ethicist Peter Singer has come to find himself. The Guardian's Mark Vernon explains why. Here's the key graph:
[Singer] described his current position as being in a state of flux. But he is leaning towards accepting moral objectivity because he now rejects [David] Hume's view that practical reasoning is always subject to desire. Instead, he inclines towards the view of Henry Sidgwick, the Victorian theist whom he has called the greatest utilitarian, which is that there are moral assertions that we recognise intuitively as true.Or to put it differently, Singer seems to be recognizing that unless there exists a transcendent moral authority, an omniscient and perfectly good God, there's no non-arbitrary reason for being a utilitarian rather than an egoist. In a world without such a moral authority nothing one does can be morally wrong, and it'd certainly not be wrong to simply live for oneself or adopt a might-makes-right ethic. However we choose to live, if there is no God, is purely a matter of taste and to say that one should be a utilitarian is nonsense. The word "should" implies a moral duty and if there is no God there are no moral duties.
At the conference, he offered two possible examples, that suffering is intrinsically bad, and that people's preferences should be satisfied. He has not yet given up on ... utilitarianism. Neither is he any more inclined to belief in God, though he did admit that there is a sense in which he "regrets" not doing so, as that is the only way to provide a complete answer to the question, why act morally? Only faith in a good God finally secures the conviction that living morally coincides with living well.
The only surprise in Singer's last sentence above is that it has taken someone of his intellectual stature so long to see it.