According to Baghdad, the Iraqi leader went on TV hours later to condemn the U.S. military action. But U.S. officials now say the uniformed man in a taped speech on state television may have been one of Saddam's body doubles.
The question then is whether Saddam Hussein, who was believed to be in the destroyed bunker, is alive.
"I don't think we'll know until we see the body and do a DNA sample," says CBS News analyst and retired Air Force Maj. Gen. Perry Smith. But it doesn't make a difference in the way the war is waged, he adds.
In either case, he says, U.S. troops will still need to invade because Saddam can be replaced by one of his sons or trusted friends.
Reporting from the Pentagon, CBS correspondent David Martin says the U.S. had very good intelligence - signals intelligence - that put senior leaders, the tight circle around Saddam Hussein in that bunker. All reports they have gotten back from the pilots are that the bunker has been destroyed.
"At the very least," Martin says, "Saddam Hussein and those around him have not been heard from, with the exception of that taped speech, since. So what that means [is] there's no one giving orders. So how much longer can this regime, which rules only by fear last if the people who instill that fear are either dead or in hiding?"
If that is true, Smith says on The Early Show, "There are a lot of uncertainties."
One scenario would be that if Saddam Hussein is gone, his military might give up and U.S. troops won't have to fight. "A little bit like [when] we went into Haiti," Smith says. "We didn't have to kill anybody. We just went in there and took over the country."
But whether Iraq mounts a unified defense or just surrenders is irrelevant, he says. "We've got to get the weapons of mass destruction. We've got to be sure these people have a chance to get back on their feet and be run by people who are not brutal dictators."
On Wednesday night, Smith explains, "The CIA found a good target, we were ready with cruise missiles and stealth fighters and we were able to go after some leadership. Once we do that, then the rest should collapse. So it was a target of opportunity. It was getting very close to dawn. You couldn't use a whole lot of time for stealth airplanes."
Gen. Smith explains the stealth fighter dropped a couple of bunker busters.
"There are a couple of types," he says. "This is a 2,000-pounder with steel casing. So it can get very deep."
The Tomahawk missiles came in from ships - both surface ships and submarines - in the Red Sea and the Persian Gulf. Coming from several sources in different directions, the missiles all landed at about the same time.
"And there is some shock and awe there," Smith says. "It's not across the whole country," he says, but "very precise."