If there were no God, a person wouldn't have a conscience. There's no reason for a conscience to evolve, so if there were no god then humanity would be just like the other animals in every way.
If religious theists are unable to demonstrate that atheists cannot justify a morality outside of the existence of their god, then some switch to arguing that our desire to have a morality and our basic sense for what's right or wrong cannot exist without a god. We might be able to find rationalizations for our behavior outside of God, but ultimate we cannot avoid concluding that God is responsible for our having a conscience because that could never have evolved naturally.
This myth reveals a serious lack of understanding and knowledge about evolution. In point of fact, we humans are a lot like animals and a number of other species have demonstrated that they have something that looks like a rudimentary conscience and a rudimentary (or proto-) system of morals. It has, for example, been observed that chimpanzees will exhibit what appears to be fear and shame when they do something that violates the rules of its group. Should it be assumed that the chimpanzee fears God? Or is it instead more likely that such feelings should develop in social animals?
It's not a surprise that something like this would evolve naturally. Morals are, basically, the rules by which our social groups function. They ensure that things are reasonably fair and that relationships run reasonably smoothly. Social groups simply wouldn't survive without rules, so the evolution of the ability to create and follow rules should be expected. Humans are social animals so it's also to be expected that, like other social animals, we would have social rules which regulate group behavior. We certainly don't need gods to explain it.
Our conscience is basically our ability to internalize rules we know right from wrong and prefer the right to the wrong regardless of whether we are being observed and regardless of punishment. Again, this is ultimately a more efficient system for social rules and the evolution of the ability to internalize rules is not the least bit surprising, especially in light of animal behavior which is highly suggestive of a rudimentary "moral conscience." Gods simply aren't relevant.
The fact that people and cultures all over the world have many similar ideas about what is moral does not justify the conclusion that there are objective standards, independent of human experience and reason, against which we are comparing our ideas. Yes, we are using some sort of standard but why assume that standard isn't a part of us? We are all more similar than different and we all share many experiences in life. Wouldn't those experiences lead to many basic and common principles regarding matters like sharing, fairness, and suffering?
In fact, the similarities in people's ideas about right and wrong over time and across cultures helps support the idea that morality has evolved. If morality is part of our evolutionary inheritance, then we should expect there to be some broad similarities and agreements. If moral rules are selected for because they help social groups survive, then it's likely that most social groups around the planet would end up with relatively similar rules of behavior the possible variety of successful high-level standards won't be that great.
The fact that our moral standards have clearly developed over recorded history is a further argument for the idea that morality is a product of human social evolution and not divine fiat. If our conscience was created by God, then why does the human conscience say different things today than it did several thousand years ago? A number of moral standards are different today than they were 100 years ago and many more a different than they were 1000 years ago.
Personally, I think that that is a good thing. We merely need to look at the biblical teachings on matters like slavery, war, and the treatment of women. Do we still follow those teachings? No. Have we changed and moved away from those teachings? Yes and we're all better off for it. Minorities have equal rights in politics, society, and business. People of different races can marry. Jews can live wherever they want. Women arent forced to remain in the home. Human moral standards have evolved because human moral standards are originally products of evolution.