This was something I was afraid of. Israel cannot fight indefinitely. The nation is too reliant upon its reserves, and they can’t stay in the field too long. They’re not professional soliders, and they have lives to get back to. (Also, taking that many people away from their jobs is going to wreck the economy.) And they’re not animals, as the captain quoted here says, nor are they barbarians. If there isn’t an attainable goal in sight, they are not going to cheerfully go off and kill.
The answer is not to back off, though. It’s the opposite. Turn everything loose and beat the Palestinians into submission. (Then, as Instapundit has said, let the Jordanians take over.) Israel can bring a fairly massive amount of force to bear, they just can’t fight a low level war for a long time.