"Is there any doubt in your mind that the Israeli army can eliminate this foe if allowed to continue?"
Continue doing what? If they are continuing what they're doing now, yes, there is no doubt Israel will NOT eliminate this foe.
They have nothing to trade, a few miles of land the Lebanese know Israel will leave anyway if there is no deal.
Hmmmm.... I guess they should just surrender, then.
As it happens, however, Hezbollah is being forced to use its stock of missiles, to very little effect; its fighters are reportedly being killed in large numbers; Iran and Syria have been recognized by the world as being behind the Hezbollah activities; the Hezbollah infrastructure in Lebabon is being systematically destroyed; and most of the other countries in the area (e.g., Egypt, Jordan, etc.) -- not to mention Europe -- are not all that exercised about it.... All in all, Hezbollah looks like it's using and losing its assets to no good purpose.
It's difficult to define the exact parameters of victory in this kind of fight. But it seems to me that the ones listed above count heavily in Israel's favor.