It actually wasn't that crazy of an idea. Many Arab countries joined the coalition and getting Israel to join it would put those Arab countries in the awkward position of fighting alongside Israel instead of attacking it, as they usually did.
The U.S. obviously wanted to keep that from happening.
Now, if you've been keeping track, the Israelis don't take kindly to threats. Or attacks. Especially scud missile attacks. Over the course of 17 days, Iraq fired 39 Scud Missiles at the highly populated coastal cities of Tel Aviv and Haifa. An estimated 147 Israelis were killed.
To give you an idea of how Israel tends to retaliate to this sort of thing, the 1972 Munich Olympics attack killed 11 Israelis. In response, Israeli intelligence – the Mossad – launched Operation (no joke) WRATH OF GOD. They hunted down every Arab plotter of the Munich massacre and killed them. For 20 years.
Only the Mossad wasn't about to wait 20 years to ice Saddam.
In 1992, they came up with Operation Bramble Bush, their plan to assassinate the Iraqi dictator. One agent, Nadav Zeevi, was tasked to find a pattern in Saddam's movements. Then, the Israelis would track the dictator to where he would spend a longer amount of time. Once Saddam settled into a location, the Israelis would have their revenge.
But instead of an air strike, Israel wanted to mount a "glamorous" commando raid, using Sayeret Matkal special operators in a kill, definitely not capture mission. One version of the proposed raid had commandos launching missiles at Saddam during a funeral.
Israel mounted crazy, balls-out commando raids in the past. Their legendary raid on Entebbe featured a caravan of cars designed to resemble Ugandan dictator Idi Amin's entourage. They flew into Uganda, landed at the airport, drove off to the terminal, killed every terrorist, and then took their hostages to waiting planes in a hail of gunfire.
Unfortunately for history, they had to abort the idea. It was difficult to track Saddam because of the sheer number of his body doubles. Agent Zeevi even thought to just watch the dictator's mistresses, but the body doubles also fooled the mistresses.
To make matters worse, a dry run in Israel's Negev Desert went horribly awry. Troops training for the raid in 1992 accidentally fired a live missile, killing five IDF soldiers. The accident led to officials canceling the operation.
They thought they might try again in 1999, waiting until Saddam was in a designated location. 40 operators divided into two groups; one within 200 meters of the location, painting the location as a target, the other six miles away, firing three Midras missiles on that target.
That plan was scrapped because the Americans and British were bombing Iraq anyway. And in the end, they didn't have to assassinate the dictator. But let their effort be a lesson: just leave Israel alone.