US Vs. Hezbollah

What if the United States did not invade Iraq but instead, went to Lebanon to intervene against Hezbollah with the intention of ousting them?
 
It may end up being as unpopular and a mess like Iraq because it would be ideal place for Al Qaeda to take advantage propaganda wise. They will claim that the US is supporting Israel and destroying Muslims especially Palestinians and get more volunteers to fight there. But I don't see the region as unstable with Saddam still in power to counter the Iranians
 
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