Actually, Singer's use of the term absolute affluence is not perfectly analogous (because the corresponding analog to the conditions of absolute poverty are those of extravagant wealth not working class wealth), but the idea itself is still valid just the same. The point is simply that once human society in part of the world reached the point where even most of those considered "poor" receive adequate nutrition, shelter, and the most basic emergency medical care (etc.), a moral duty arises whereby helping the less fortunate should be more important than self-centered concerns about increasing one's wealth relative to others in the manner that different levels of affluence are defined in wealthier nations.
It is important that Singer acknowledges the difference between ideals that people should uphold and ideals that people must uphold, because it is likely impossible to establish a logical justification for compelled charity, regardless of the moral imperative.
In fact, U.S. law also recognizes that distinction as well. To use Singer's first example of the rescue of the drowning child, there is absolutely no legal duty to conduct any such rescue, provided that the non-rescuer is not related to or in charge of the child and had no part in causing the child to fall into the water in the first place. However, there certainly is a moral duty to assist the child whether or not that duty is enforceable at law.
Likewise, charity in the form of assisting the poor of other nations cannot be mandated. However, from an objective moral perspective, the situation is analogous to the individual faced with the obvious moral duty to intervene to prevent the child from drowning. Singer correctly points out that the lifeboat ethics theory is inapplicable simply because none of the assistance to Third-World nations at issue poses any threat to the welfare of more affluent nations. Similarly, the notion of caring for the poor of this country is specious on two different levels: first, by virtue of the faulty comparison between the relative poverty faced by First-World poor and the absolute poverty of Third-World poor; second, by unfounded a-priori assumption that similarity in race, skin color, ethnicity, or national origin is a valid determinant of whether charity is morally required.
Singer reserves his most detailed refutation for the anticipated argument that to provide assistance for starvation where overpopulation is a simultaneous concern only perpetuates the problem and increases its magnitude. The author acknowledges the logical soundness of the conclusion but challenges the premise that overpopulation today will necessarily continue at the same rate or increase after the receipt of aid from outside.
Specifically, Singer points out that high infant mortality is the main reason that impoverished people tend to have large families. In fact, Singer presents evidence that as starvation and poverty decrease and basic medical care becomes more available, less impoverished people tend to reduce the size of their families proportionately. Therefore, it is not the case that providing assistance today necessarily perpetuates or exacerbates the problem in the future. Singer also suggests that assistance need not be restricted to providing money or food, but in the same manner of the proverb about teaching a man to fish instead of merely feeding him a meal, Singer outlines some of the other approaches to charity that could conceivably solve many of the problems of the absolute poor, or at least improve their living condition considerably. In that regard, Singer emphasizes the importance of encouraging governmental reform where institutional problems contribute to the problem, in addition to providing education and redressing age-old cultural limitations on the role of women in some of the most impoverished societies where women are believed to serve only one purpose: to bear children.
Possibly the most crucial point made by Singer is the importance of providing effective contraception to address the overpopulation issue that only worsens many of the problems of the absolute poor. For that reason, Singer would undoubtedly have been horrified by the nonsensical position taken by the most recent Right-Wing-oriented presidential administration of George W. Bush that specifically prohibited federal funding for charitable efforts if they included contraception or education in their use.