Well, before we can get to the meat of the conversation, we have to define "morality".
It seems to me most of us are in agreement that morality is the distinction between what is necessarily "good" and "evil", "right" and "wrong", "just" and "unjust", and so forth.
From this premise comes the next part of the argument: who defines morality?
If we assume a lack of existence in God, then there can't be morality, as nothing exists to define it for us. Without God, morality simply becomes a socially-constructed, mutable thing, vulnerable to the faults of human beings. At any time, murder can be universally justified, as theft, jealousy, adultery and other immoral behaviors.
But, as it turns out, the "moral but not religious" camp draws their conclusions of right and wrong from God. Without God or, at least, a similar explanation, their entire concept falls apart—as morality would become entirely relative and the world would be disorderly. Then if we ask them where their concept of right and wrong came from, they'd say it came from their parents. And from their parents, their grandparents. So on and so forth.
When you've reached the conclusion of their family tree you'll find that their values, their morality, their compass, came from God. All the Ten Commandments will be in there and very likely will be reinforced by the role religion played in their culture, in their family, etc., and they will share common beliefs.
So, the long and short of it is: no, you cannot be moral without God. Morality is God. It's what he gave to us. It's what makes us unique. Animals don't have morality. A lion cannot decide it's immoral to eat a gazelle and stop doing that. It has no sense of morality. We're rational creatures endowed with free will who were given commands by God in how best to use our free will. Not only for ourselves, but for our neighbors.