Ruled for decades by a brutal and secretive regime, Iraqis are distrustful of official statements and so gripped by fear that it will take time to persuade them that the Iraqi dictator won't return to power, said Moniem Al-Khatib, a former Iraqi diplomat who lives in London.
Among Americans, polls show that many regard the capture or killing of Hussein as key to the success of the war in Iraq.
If the United States and its allies succeed in destroying the regime without capturing or killing the Iraqi leader, the war will be viewed as a success by a public that wants, above all, to be free of any threat from Iraq, says Steven Kull of the Program on International Policy Attitudes.
Yet, the failure to eliminate Hussein would "tarnish the image of success," Kull said.
President Bush launched the war March 19 with a bombing raid on a Baghdad dwelling where Hussein was believed to be meeting with other regime leaders. In the weeks since, however, administration officials and U.S. military spokesmen have sought to play down the importance of catching or eliminating Hussein, saying the goal of regime change was not about just one person.
But U.S. and British officials also acknowledge a perception problem in persuading Iraqis that the regime is finished as long as Hussein is unaccounted for. Defense Secretary Donald H. Rumsfeld spoke Monday of Iraqis having to come to a "tipping point," when they realize "that the guy's going to be gone, that regime's going to be over."
Asked by CNN's Larry King if capturing or killing Hussein and his sons was imperative to changing Iraqi perceptions, Britain's defense secretary, Geoff Hoon, replied: "It's certainly part of what we need to do in order to finally remove this regime from Iraq."
Just removing Hussein from his position of leadership is unlikely to assure Iraqis that he won't reappear to reclaim power, especially if he manages to flee the country or goes underground.
Iraqis have become accustomed to their rulers living in the shadows, with the heavily guarded Hussein rarely showing himself in public while exercising total control over the country through an extensive security apparatus. Also, they can recall that his Baath Party developed as an underground movement before coming to power.
A senior administration official said killing or capturing Hussein "will make a big difference. That would be what gives the Iraqi people confidence that it is finally all over, that the old regime won't come back to haunt them."
Kanan Makiya, a prominent Iraqi exile and the author of Republic of Fear, a book about Iraq under the rule of Hussein's Baath Party, said on Fox News Sunday that "physical, palpable evidence that he himself is either dead or captured ... is very, very important."
"I would say that a necessary condition for the fear to remove itself is that the key lieutenants in and around Saddam's inner circle and himself be captured or somehow find their fate be sealed in some other way," Makiya said.
Al-Khatib, the former Iraqi diplomat, recalled a previous regime change in Iraq in 1963, when former president Abd al-Karim Qassem was overthrown and killed. A lengthy film clip of his bullet-riddled corpse was shown repeatedly on Iraqi television.
The next year, while serving as a translator during a foreign trip by Qassem's successor, Abd al-Salam Aref, Al Khatib asked him why the gruesome display was necessary. "His answer was, 'The people of Iraq would never trust us unless they see a picture of Qassem that [shows] he is dead.'"
Hussein's violent history is one reason not all of his opponents overseas want to see him killed.
"From an Iraqi perspective, it's necessary for the healing process that he is captured and tried - and tried by his victims," said Muhannad Eshaiker, an Iraqi architect who has worked with the State Department to prepare for post-Hussein Iraq.
"Put him on TV. Let him defend himself in public. Show his victims, and let the world hear all the crimes he's committed," Eshaiker said. "Let Iraqis know a new Iraq is not going to be bloody."