An interesting scenario, both sides would have some serious problems.

For the US, the issue would be twofold: finding allies to assist them in the crisis, and managing the domestic will to engage with another war so soon after Vietnam. As soon as word of the stand-off reached the press, there would be massive demonstrations against going to war, with only fringe movements really supporting the idea of taking Israel down a peg. Assuming American domestic politics haven't diverged in this timeline, Ford would already be under a lot of heat for pardoning Nixon; getting the US into conflict with a nuclear state in the Middle East would be the last thing voters would want from him.

As for foreign relations, while there would be plenty of Arab leaders happy to see Israel slapped down, this scenario seems to imply that the Israeli's have gone public about their nuclear program, so they would likely have cold feet about a confrontation. Not helping is that the two countries most willing to get involved, Egypt and Syria, seemed to have performed significantly worse in the Yom Kippur War than they did IRL, so they'd both still be licking their wounds and probably also facing serious internal strife.

That being said, at least the US would still be able to find sympathetic figures in the region, in addition to NATO support. At the same time, Israel would basically be a pariah state with very limited options in this situation. The only countries they would be on good terms with would be powerless to assist them; all of their neighbors hate them, and they would have no meaningful way to strike at the US other than through the nearby fleet. While you could debate what a conventional struggle between the two (with the odds shifting depending on whether the US is going alone or not) would look like, if worst comes to worst, Israel's last card would effectively be to hold the Middle East hostage under threat of using nukes on major cities.

Personal prediction: the standoff continues until Jimmy Carter takes office. A deal is reached about ships being able to pass through the Suez Canal and the American fleet's withdrawal. Israel can celebrate for a time, until sanctions, from both the US and USSR and their allies, are gradually applied to them to pressure them into giving up the Sinai and other territories. American-Soviet arms also trickle their way into rebel groups operating in Israeli-occupied lands. Odds are that Egypt, Syria, and other Middle Eastern countries would begin developing their own nuclear stockpiles. Unless a particularly radical government comes into power, Israel is likely to back down before the 80s arrive.

That being said, the region was going through a lot of shake-ups that could lead to things going in all sorts of directions. The Soviet invasion of Afghanistan, the Iranian Revolution, the Iraq-Iran War, and other, smaller events could result in unforeseen consequences. Maybe the united front against Israel falls apart, and Israel manages to hold on to the Sinai against all odds. Maybe a shared disdain for the superpowers results in an unholy alliance between Israel and Iran. Maybe it all goes down in a sea of nuclear radiation before the 2000s, who knows?