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It is not exactly about many countries in the middle east wanting to get favors from Israel, but rather they wanting to keep good political and commercial relations with the United States. The white house can be either occupied by a Republican or a Democrat, it does not matter. In the end, the most important ally of the United States will be Israel, thus those countries which want to keep some pragmatic way open for them to deal with the USA and the European Union find themselves in a position on which they have to be friendly towards Israel or at least not to show any kind of direct aggression against it.
Also, the United Nations may have some power, but it is limited... The real power stands within the presidency of the countries with the capabilities to deploy a high number of units abroad, and those which keep military bases around the planet. Anyways, time will tell how this nasty situation continues to develop.
A perpetual cease fire is very unlikely to happen, in my opinion, what Hamas did and what the IDF did to the innocent of Gaza won't be forgotten by neither of the sides.