Does Adam really go so far as to try, in Gen 3:12, to put some blame on God, for giving him Eve?

Perhaps not explicitly, but he comes close; why else should it be relevant to point out that God gave him Eve, if doing so does not further removes blame from Adam himself? Notice that Adam is actually not incorrect when he implies that Eve did not perform her function, as his help meet, properly. Indeed, she did betray Adam. But she was the one responsible for her own failure, through the exercise of her free will, just as Adam was; God could not be saddled with their failures. To blame God for Adam’s own sin is something that one can imagine the serpent whispering to Adam.