When the Israelis began their campaign, their avowed plan was to push Hezbollah 35 miles to the north, beyond the Litani, and destroy most of its arsenal. Now, suddenly, after realizing that Hezbollah wouldn't crumble under the bombs :

From BBC News http://news.bbc.co.uk/2/hi/middle_east/5214046.stm

Mr Peretz said a zone in southern Lebanon would be maintained "under the control of our forces if there is not a multinational force". He did not specify whether Israeli troops would remain there but insisted they would "continue to control [Hezbollah]" in their operations.
Israeli government sources have estimated the width of the zone at anything from three to 10km (1.9-6.2 miles).

What a daring, dazzling plan !

I agree with your assesment, George O Well, the Israelis realize that they can't take out Hezbollah with their misguided strategy. Behind all the Olmertian and Peretzian tough talk, none of the Israeli civilian and military leaders want to lauch a full-scale ground invasion of Southern Lebanon.
And, as they don't wish to lose face, they call Washington for help.

On the other hand, if none of the parties involved are able to agree on the cease-fire and the international force in South Lebanon, the conflict will worsen, as no one will want to back down and become the "loser" in the eyes of public opinion.