Don't blame Bush for Israel's failure. He was giving them all the time they needed until he realized that Israel's leadership didn't have what it takes.
Israel's failure in Lebanon and Bush's failure at the UN are separate failures each deserving of blame.
I doubt Bush would appreciate if there was a higher authority who decided that the Iraq war ends tomorrow because Bush has not come to a satisfactory conclusion after three plus years.
I doubt Israel asked for more time. My guess is that Israel wanted to limit the body count, and decided that plan B would stop the rockets for the forseeable future, and that Hezbollah rearming would now violate a UN resolution, and give it a longer leash in the future, if such is the case. One can criticize that, but then it is not our relatives at risk.