Strategy Page gives us a history lesson on how Hezbollah came about and why it wields so much power. Their analysis also discusses Israel's options which SP thinks are limited to two:
The Hizbollah attack left Israel with two options. They could either launch a massive invasion, and overrun all of Lebanon and Syria, or do what they did (to encourage the Lebanese and UN to deal with Hizbollah.) The trouble with the second ("small war") option is that it takes longer, and that leaves Hizbollah intact for longer. But the first ("big war") option would leave thousands of Israeli soldiers dead, and involve the occupation, for months, if not years, of Lebanon and Syria. That strategy would involve handing Lebanon back to its elected government with the understanding that there would be no more Hizbollah. But there would still be the a Shia minority, and within that minority there would still be Shia radicals who took orders, or at least direction, from Shia radicals in Iran.
Syria has to be overrun because, if you don't, Hizbollah can retreat to there from occupied Lebanon and set up shop in Syria. Take Syria and you eliminate any refuge (except Iran, where at least the senior Hizbollah people would flee to). While the Syrian military is no pushover, their armed forces have fallen apart since the end of the Cold War, and Soviet subsidies.
The column closes with this:
The "big war" strategy has other costs. Mobilizing the entire Israeli armed forces means shutting down much of the Israeli economy, because so many key people are reservists. There is also the risk, however slight, of other Arab states declaring war on Israel. This risk is slight because those other Arab states are Sunni Moslem, and welcome the removal of Iran backed Shia entities (Hizbollah and Syria). But the risk is there.
There's always risk, it's a question of which one you estimate will do you the most good. Israel still has the "big war" option available, and Lebanon and Syria know it. If the small war option doesn't work out, Hizbollah, Lebanon, Syria and Iran know what comes next.
The whole piece is very much worth reading.