I was not familiar with that! This is after the United Kingdom tried to pawn it off to the United States, so it was sent to the United Nations...and I guess this was the United States saying, "Okay, so the United Nations solution isn't working, so we guess we'll have to take charge after all". United.
Still, short of sending in the Marines, there's not much that the US could even do. Though I guess they could do that. And something like 20,000 Marines with proper training, equipment, and support could almost certainly make both sides shut up and play nice (at least if/until the guerrilla war and popular uprisings started, like against the British presence).
Still, though, it seems very unlikely. As the article you linked mentions, most of the State Department was firmly against Israel at the time (not for any particular ideological reason, they just thought the Arabs collectively were more important. Actually, you can look at OTL and basically between recognizing Israel as a country and starting to sell arms in 1968, there's a 20 year period during which the US had effectively no relationship with Israel at all. Plus, there's no compelling reason for the US to get their noses dirty in a little region that had already shown itself to be more trouble than it's worth...though I guess it's possible that there could be folks in State who see this as a way for the US to stretch some muscles and begin its career as World Police.
Even then, I can't see it ever becoming anything more than something Philippines-esque; even in the face of mass migration of American Jews to Israel and resulting Amerification of the state, it's still too remote to incorporate (especially since it's not little dinky islands in the Pacific, it's a strip of land on the other side of a sea that's accessed by passing through a narrow strait on the other side of the Atlantic).
Still, as an American protectorate, it would "advance things in the region by 20 years" in that the Arabs would immediately go to the USSR without all this pussy-footing around with Arab Nationalism becoming Arab Socialist Nationalism and whatnot. It also butterflies the Suez War, but I don't know enough about decolonization to predict what that could do.