hezbollah is supported by a huge amount of lebanese citizens. virtually all the shi'ites support them, about half of the sunnis do and 70% of the christians voted for them in the last election. an israel-led attempt to get rid of hezbollah would have resulted in an extremely bloody revolution. israel's disastrous invasion of lebanon in 2006 actually gave hezbollah more support than it already had.
Nigeria says troops destroy extremist camp, rescue 178 people (AP)
from the article: Obama backs embattled Lebanon PM, after Hezbollah topples government