(Maybe the Israeli are not planning a full scale ground invasion until they notified U.S)
I doubt a ground invasion will happen, and if it does it won't be any time soon. Something like this takes a lot of time to plan, and I doubt that Israel was expecting to take this action. Plus they are very weary of Hezbollah which had years to prepare for an Israeli invasion.
You might be right, there may not be a full-scale ground invasion of Lebanon. But one thing is certain, if Hezbollah is not thoroughly decimated right now, they'll rev up their attacks on Israel and if the government is seen to be passive, it will be the end of Olmert's administration and would pave the way for return of "Bibi".