She should have to clear it with the father and if they can't find him, then she can carry it to term.
What if she claims that the child was conceived in a one night stand with a man whose name she does not know and has no contact with.
This thread is talking about spousal consent; that would mean her husband, not just the father of the child.
What right does the husband have to help determine the fate of this child if he is not its father? He should certainly be able to sue her for divorce, but thats a totally different matter.
And if he is the father and there is father's consent, a desperate mother could just make the claim I do above, thus completely bypassing father's consent and rendering the law toothless.