Andrew, I think U.S. and Israeli interests are perfectly aligned on this one. Remember bin Laden’s refrain about “the strong horse and the weak horse” – the fact that people (particularly those targeted for jihadi recruitment) are always drawn to the strong one. That’s the language jihadis understand, and no other.
One can always say a robust response to radical Islam’s atrocities helps Hamas, al Qaeda, etc., to recruit. But recruiting is aided at least as much by successful terrorist attacks to which the response is too meek. The people sitting on the fence — the ones who are sympathetic to jihadi aims but ambivalent about jihadi methods — are attracted most of all by the prospect of being with a winner. Sure, a robust response that communicates the resolve to keep fighting until the jihadists are crushed may bring in a lot of new recruits; but it also scares off a lot of prospective recruits while killing off the experienced ranks of a terrorist organization — making the organization, on the whole, a less dangerous killing machine. That’s why it remains the right thing to do.
Some conflicts are deep ones, pitting survival against an incorrigible evil. Those conflicts cannot be resolved until one side wins and one side loses. The U.S. strategic interests in the Middle East will suffer as long as there is doubt about whether Israel is here to stay. That means fighting hard until the will of those who are beyond accepting Israel’s existence is broken and their capacity to project meaningful power is destroyed.
If we get to the point where those who are left accept Israel’s existence, however reluctantly, and are willing to negotiate their grievances through ordinary politics and diplomacy, then we can worry about a broader range of strategic interests where the U.S. and Israel may not align. But not until then. Until then, it’s in our interest for Israel to crush its mortal enemies … and not give those mortal enemies yet another breather so they can regroup for yet another round in a year or two.