It's an interesting problem, given that Israel itself has no faith in winning a prolonged war. The entirety of Israeli military doctrine, training and tactics has been oriented to waging brief and intense wars.
Basically, Israel's conscription policies can mobilize huge numbers of troops. But only for very short times. There is only so much manpower available. Take a significant portion out of the civilian industrial complex, and the country is in trouble, economic dislocations follow.
Equally, doctrines are based on massive expenditure of munitions. In the war on Lebanon in 2006, Israel was actually running out of jet fuel and cluster munitions and required emergency resupply from the US. Lebanon is by no means a huge country, so the rapidity with which Israel exhausted its stores is stunning.
Given the logistical limits, I don't see Israel successfully waging a prolongued war. Tanks need gasoline, jets need fuel, guns need bullets, troops need transport. The further afield these go, the more supply lines are needed, and the more exponentially expensive these supply lines become. Israel simply doesn't have that capacity, never needed it, never bothered to develop it, cannot manufacture it out of nothing, and in all probability couldn't develop it over time.
It's really hard to see an Israeli campaign successfully marching on Baghdad or Mecca or Tunisia. And by this, I mean a real campaign as opposed to the smash em up raids we've seen.
I'd also suggest that actually holding any significant quantity of territory is outside of Israel's capacities.
Whether Arab states would hold up is another question. Generally, the poorer or 'weaker' state with fewer military resources tries to have short intense wars, because it doesn't have the resources for a prolongued one. Obviously that's not on. The Arab states would have to rethink their military doctrines, such as they are.