In fact, anytime we have showed restraint — using battleship salvos and cruise missiles when our Marines were killed, our embassies blown up, and our diplomats murdered; allowing the killers on the Highway of Death to reach Basra in 1991; letting Saddam use his helicopters to gun down innocents — we have earned disdain, not admiration. In contrast, the hijackers chose not to take the top off the World Trade Center, but to incinerate the entire building — proof that they wished not to send us a message but to kill us all, and to kill us to the applause of millions, if the recent popularity of Osama bin Laden and his henchmen in the Arab street is any indication.
No discussion concerning the survival of Saddam Hussein without mentioning the role of former General Colin Powell's poor advice to President Bush and Bush's ill-advised decision to end the original Gulf War on February 28, 1991--before the surviving core of the defeated Iraqi army (mainly two divisions of the Republican Guard with most of their equipment) could be cut off and destroyed, or captured and disarmed.
Bush made his decision at the forceful behest of General Colin Powell, then-Chairman of the Joint Chiefs of Staff. Powell reportedly told Bush and the rest of the White House "High Command" that the remaining Iraqi army was totally defeated and in full retreat and that further attack would be a slaughter, both "UN-AMERICAN and UN-CHIVALROUS".
General Norman Schwarzkopf and his generals were collectively against the premature cease-fire, estimating one to three days more would be needed to cut off and finally trap the Republican Guard survivors (keep in mind we're not talking about going to Baghdad, but only blocking the road from Basra to Baghdad, which the U.S. 24th Mechanized Division and 101st Airborne were poised to do). But unfortunately, Schwarzkopt did not push this view to Bush, to whom he reported directly, a serious error of omission. No more Iraqis needed to have been killed. They had only to hoist a white flag or simply abandon their vehicles and equipment, and walk away. Powell knew all of this.
The Brits were furious about the cease-fire. So were the Saudis, Qataris and other Arab Gulf countries. In fact, Newsweek reported British Gulf commander Gen. Sir Peter de la Billiere went "ballistic" and British Foreign Secretary Douglas Hurd--who happened to be in Washington--jumped Bush about it immediately, unfortunately to no avail. Had the Guard and it's equipment been finally captured or destroyed, the Shiite rebellion in the South would probably have succeeded. Combined with the simultaneous Kurdish insurrection in the north, it was highly likely that Saddam would have chosen to take a hike and would not be a problem today. Had that happened, thousands of civilian lives would have been spared.
Saddam's survival led to the continued UN sanctions on Iraq. These have grievously persecuted a population that was powerless to overthrow a tyrant that the U.S. allowed to stay in power. Pre-Gulf War, this population greatly admired America and Americans.
This is essentially speculation with little basis in fact. The goal of Op Desert Storm was to kick Iraq out of Kuwait while destroying most of its military equipment. The goal was not to completely destroy the Iraqi army because this would have left Iraq vulnerable to invasion by Iran. The first Bush Administration was hoping that the remaining Iraqi army officers would turn on Saddam and remove him from power. Unfortunately, the army didn't rebel and Saddam stayed in power.