According to a former senior CIA official, who also spoke on condition of anonymity, Dayan sought an urgent meeting with Prime Minister Golda Meir and secured her authorization to arm 13 intermediate-range Jericho missiles with nuclear warheads. Eight F-4 Phantom fighter aircraft were also to be given nuclear arms, former senior U.S. officials said.
Avner Cohen is the the professor of International Studies at Middlebury College in Vermont. He specializes in Israeli Foreign Policy and Israeli nuclear history. In a 2003 New York Times op-ed piece, he suggested that the situation you asked about may have occurred in order to compel the U.S. to open a supply line to Israel. The main piece of evidence in his op-ed piece came from a recent interview of an Israeli official who worked during the war. Cohen considers the Cuban Missile crisis and this event to be the two moments when the world was at "the brink" of nuclear warfare.
It was in the early hours of Oct. 9 that senior Israeli military leaders brought up the idea of using Israel's doomsday weapons. By that time Israel had lost some 50 combat planes and more than 500 tanks -- 400 on the Egyptian battlefield alone.
...Later that morning, at the end of a somber briefing before the war cabinet, Mr. Dayan raised the nuclear option with the prime minister. No detailed record has surfaced as to what exactly Mr. Dayan proposed, but we know he gave an overall assessment that Israel was fast approaching the point of ''last resort.'' And certainly Mr. Dayan wanted the United States to take notice that things had reached such a point. That he meant using nuclear weapons (albeit in coded language, as at the time nobody dared call them by name) was confirmed in an interview last week by Naftali Lavie, who was Mr. Dayan's spokesman during the war.
...American intelligence had signs that Israel had put its Jericho missiles, which could be fitted with nuclear warheads, on high alert (the Israelis had done so in an easily detectible way, probably to sway the Americans into preventive action).
Mr. Kissinger instead started to arrange air supply to Israel, and within three days a tremendous United States airlift to Israel was in action. The tide was turned. By Oct. 21 the Israelis were within 20 miles of Damascus and had crossed the Suez Canal, encircling the Egyptian Third Army. A permanent cease-fire was established within a few days.
The state of Israel did indeed threaten the use of atomic weapons unless the united states re armed them. In response Richard Nixon gave them unlimited access to the arsenals of western Europe, which they drained to the point that, had the soviets known of it and rolled, there wouldn't have been anything left to oppose them. The 'official' answers to this question do not exist because posing the question results in nothing but silence. However, study the low level documentation from the time, like the force ready inventories of the western European American force of the time period and the truth of what occurred is evident.