While there are no doubt many who support Hezbollah, many don't. However, up to now, it has been easier for them to live with Hezbollah, than to deal with them.
Israel is changing that political calculus. In addition to stomping Hezbollah wherever they can be found, they are also showing the rest of Lebanon, and the world, that it's best not to let terrorists live among you.
"...and accordingly all experience hath shewn that mankind are more disposed to suffer, while evils are sufferable than to right themselves by abolishing the forms to which they are accustomed."
- Thomas Jefferson, U.S. Declaration of Independence
It is a hard lesson to learn that evils must not be suffered. There is always a price to pay.
Shalom.