One thing to point out re Vietnam is if this happens as an alt 6 Day War I could see greater likelihood of US intervention. In 1967 the war in Vietnam, while escalating, hadn't hit its point of being very unpopular since Tet hasn't happened yet.
I think the war would rule out any ground troops being deployed but that wouldn't stop US aircraft with the carriers in the Med from running missions while long-range strategic aircraft fly sorties over Israel. If it looks too late to turn the tide those same assets could run cover for any evacuation efforts.
Yeah, I'll second this. The Sixth Fleet is right there, and they'd have
America's Carrier group plus the assets of the US Air Forces Europe. Meanwhile the Royal Navy has
Hermes in the Red Sea, and several other assets nearby, particularly Akrotiri and Dhekelia (with two squadrons of Vulcans at RAF Akrotiri, and any refugees would probably be sent to Cyprus before going onward (oh the irony.) Considering that they were prepared to intervene if Egypt closed the Strait of Tiran to Israeli shipping, if the situation looks remotely dire, they'd intervene.
Hell, if the situation lasts long enough, the Beira Patrol might be sent to the Red Sea to support
Hermes, with their collective Buccaneers being used for ground attack and strike missions while Sea Vixens fly CAP.