It's 1970, so Nasser's still alive, but he'll be dead in a few months. Nasser OTL tried hard to bring the war to mediation, vainly wanting a unified Arab line. His successor, Al-Sadat, is going to be more critical of Syria's role, and will only support Syria because the army would. Any mistakes, and he can use that against the dissenting officers later.
Israel will absolutely not sit it out. Its neighbor with the longest, most important border is about to turn hostile. The Hashemites may have been Israel's enemies prior to 1990, but it was a sort of respectful rivalry, with Jordan knowing it can't really fight Israel and Israel learning the hard way in 1968 that just because Jordan lacks the numbers, it won't be easy to invade.
A Palestinian takeover will completely wreck that arrangement. Jordan would become significantly more hostile under a fedayeen junta, and the already-porous border would let in a floodgate of raids and commando attacks.
IOTL, Syria amassed its tanks at the border, ready to move in and help the Palestinian forces. The Israeli air force flew over the Golan Heights and right next to the Jordan border to send a clear message; "cross that border and we will intervene". Syria got the message and backed down in a hurry. And in case you think Israel was bluffing, think on this; a lot of Israel's wars and actions have relied on fait accomplis to force its enemies to accept a current reality or fight it. At times, such actions have backfired greatly (the 1982 invasion of Lebanon), but for the most part, it worked well. Israel just needs to shatter the Syrian army as it rolls into Jordan, then pull back when the Syrians are forced to fall back and lick their wounds.
The USA and Britain will absolutely support the Jordanian monarchy in this fight. Jordan is a moderate state, and its loss or change would destabilize the region. There were sightings of British paras in and around the Jordanian royal palaces alongside Jordanian forces. The USSR cannot officially condone or condemn the invasion, as both Syria and Jordan have good ties to the USSR, even if Syria is officially a Soviet ally/client. Saudi Arabia will pull out the stops and flood Jordan with money and supplies to keep the Syrian army from winning.
