This always struck me as wrong, not because AIPAC isn't powerful, but because Walt and Mearsheimer (and Andrew) don't seem to understand what makes a powerful lobby group powerful. The most powerful lobbies, over time, are those that lobby for causes that are already popularamong the American people.
Walter Russell Mead understands this phenomenon, and has written about it many times. I asked Walter the other day to answer Andrew's rhetorical question. Here is what he wrote:
Full-throated support for hardline Israeli positions is a populist position in American politics -- like full-throated support for a fence on the Mexican border. It is a foreign policy idea that makes elites queasy and that they try to steer away from, but support for it is so strong in public opinion, and therefore in Congress, that presidents have to figure out how to work with this force rather than taking it on directly.
Lobby groups like AIPAC play a role, because most politicians do not want to be branded "anti-Israel" by AIPAC. The reason is that getting called anti-Israel by AIPAC weakens your support among pro-Israel gentiles. But if gentiles don't support hardline Israeli positions (like releasing convicted spy Jonathan Pollard), all the alleged mighty power of the Israel Lobby vanishes in a heartbeat.
The Israel Lobby is all powerful when it has gentile public opinion behind it; it is a much weaker creature when it doesn't. What Netanyahu demonstrated in Congress was not that he has the backing of the Israel Lobby. It was something much more important and, depending on your viewpoint, more alarming: he has the backing of the American people.