People are getting the reasoning a bit confused here. Israel didnt stop because they wanted a cease fire, and they didnt stop because they thought Obama would do anything different. They stopped it for Obama's sake - most probably at the behest of the US. The US just want to ensure that Obama has a smooth inauguration and everyone can latch on to this whole feel-good crap "change is here" without any immediate contradictions.
Truth is if the war continued while Obama was in power, he would have endorsed it. This would cause him to lose a lot of popularity in the world. This way, the war is over, he can word things nicely for the time being showing his "humanitarian" side.
Basically for Obama, this was a bit of a headache and he called in a favour - Israel owes them the odd favour.