I think that there will eventually come a day when the Egyptians hear enough of the stuff that is going on in Gaza that they will think it their duty to help their Muslim brothers. I'm not saying that this is right or how I look at it; I'm just saying that this is how they're going to look at it.
I know there are protests against the government being too Muslim going on in Egypt right now, but I don't think that's going to last too long. As soon as the government shies away from some of the more hardcore tenets in ultra conservative Islam, the protests will stop.
Yes they hate Israel to the core, but no, they won't simply because they know they will fail miserably, again. Israel is better equipped and better trained and have on numerous occasions shown that Arab numbers mean little, besides Israel also has nukes. I know the Arabs can be stupid but they can't argue with nukes that's for sure.
Egypt has way too much going on right now to plan and carry out an attack on Israel. The military and government have to figure out how to stabilize their own country so they can govern smoothly and keep things in control. They don't want to take the risk of starting a war right now.
No, I do not believe that Egypt will attack Israel. Though Egypt has disagreements with Israel, Egypt is not typically an aggressor, and Egypt has so many internal problems, such as its economy, that I don't see it happening. Also, I doubt that Egypt would want to be seen as an attacker in the world view.
Although Israel's offensive action has been met with tumultuous Egyptian protest, the probability of Egypt attacking Isreal is low for several reasons. Ultimately, Egypt's economy is in a condition contrary to a country with the ability to wage war, as wars cost. Further, though the people protest vehemently, Egyptian leaders are less aggressive in the pursuit of war at this time, as depicted in the Washington Post.