If Israel actually conducts a full scale war... that actually involves a ground invasion, then Damascus would probably fall within 3-4 hours (at most).
As for the rest of Syria? I dunno if Israel would want to occupy the rest of it.
With callups of reservists, Israel certainly wants to have it look like it will carry the war to Syria...but Syria has responded to pressure like this in the past.
The rest of Syria is insignificant. All Israel has to do is to capture Damascus. Its pretty damn close. Its like driving from Washington D.C. To Philadephia.