On principle, no, there's no inherent reason a non-religious person can't be moral. But I think certain declines in morality in the US now are a result of the decline of Christianity, namely the complete inability to forgive amongst people under a certain age, even for the smallest infractions. I forgive other because I would like to be forgiven, that fits as a part of a secular logic based morality, but it's also something that was drilled into my head when I had to go to Sunday school as a kid so that might have something to do with it too.
I must express some confusion here. Surely when we engage in moral reasoning we must be reasoning to a Good upon which we are ourselves dependent - if we are not, then you don’t really think it’s objectively good for anyone to agree with you. If we are, I see little difference between this Sovereign Good and God.