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...