The grimly serious battle for public opinion waged by President Bush and Iraqi President Saddam Hussein has entered a new and perhaps decisive stage with reports that U.S. bombs killed Iraqi women and children in a Baghdad air raid, according to experts on public opinion and war.

At stake for Bush is whether the war with Iraq continues to be seen by the American public as a "just" war -- or just another Vietnam.

The stakes for Saddam are equally high. The deaths could further intensify American antipathy toward him if it is found that he had deliberately placed civilians at risk in a military facility. Or they could elicit sympathy for Iraq in the United States, or perhaps more importantly, in the allied nations and the Arab world.

"But it all depends on how the situation unfolds," said John Marttila, a leading Democratic pollster who recently completed a national survey on attitudes toward the gulf war. "There will be suspended judgment for two or three days until this is better clarified, if it ever can be clarified."

Before the bombing incident, surveys consistently found that the U.S. public seemed willing to accept civilian Iraqi casualties because most Americans believed them to be the unintended victims of allied attacks at purely military targets.

"That message has come through clearly to the American people," said Thomas Mann, director of government studies at the Brookings Institution. "The American people have been told that we are engaged in a legitimate use of force and we are using it in a humane way."

The latest Post-ABC News poll completed Tuesday found that six out of 10 persons questioned said the United States was "making enough of an effort to avoid bombing civilian areas."

Just one out of eight -- 13 percent -- said the United States wasn't doing enough, while 22 percent thought the allies were making "too much of an effort" to avoid civilian areas.

"I think there a pretty broad acceptance that civilian casualties are inevitable and there's a percentage of people who think that {civilian casualties} may be the way to end the war," said Burns Roper, president of the Roper Organization. "I don't see that as a serious problem at the moment . . .unless it turns out we've been lied to" about the extent of civilian casualties and U.S. efforts to avoid them.

"The only way this incident would have a serious impact is if there were evidence that we knew it was a civilian target and it was deliberately hit or that we acted with reckless disregard for civilian targets," said William Schneider, a political analyst at the American Enterprise Institute.

"So far, I don't think there is convincing evidence for either."

Historically, civilian deaths appear to have little influence on public support for a war.

"The number of civilian casualties didn't make much of a difference in Vietnam or Korea," said John Mueller, a professor of political science at the University of Rochester and a leading scholar on war and public opinion. "But it may be different in this case because there is little animosity toward the Iraqis, just toward their leader."

Until those bombs fell yesterday, Americans had rallied around Bush and the war in large numbers and with an intensity that surprised even longtime students of public opinion in wartime.

Experts generally agree that U.S. public support for war rests on three legs. The first, and perhaps most important, is the cost of the conflict, as measured by U.S. casualties. The second is overall support for the reasons the war is being fought. And the third is public confidence in the competence of those who direct the fighting.

During the first month of the campaign, Bush managed to piece together a strong coalition in support of the war based largely on surprisingly low allied casualties, a deepening national consensus that Saddam had to be removed and that the war was the only way to do it, and growing support for the way Bush and the Pentagon were waging the war.

One result is that 78 percent of those questioned in the latest Washington Post-ABC News poll said they supported the decision to go to war -- even though most also believe that a ground war is inevitable and that many U.S. casualties would result.

Another is that three out of four in a recent Gallup poll believe the conflict in the gulf is a "just" war, compared to just 25 percent in the same poll who expressed a similar view of Vietnam.

The way the bombing incident could change those attitudes may be in undermining public confidence in the way the war is being handled, public opinion experts said.

"One of the lessons they should have learned from Vietnam is the credibility gap, said Bruce Jentleson, a political scientist who has studied public attitudes toward war. "There's a difference between giving out limited information and misinformation.

"The press doesn't like limited information but the American public doesn't seem to be bothered very much by that. But if it starts to become misinformation or intentional deception, then you have a credibility gap problem and the trust of the public could be broken really quickly."

Still, Jentleson suggested that "the American public may not be bothered by this incident unless it becomes a pattern."

Jentleson and others suggest the bombing could renew concerns about the justifications for the war -- the second leg holding up public support for the gulf conflict.

"It will raise questions about our purposes and our claim for a moral basis for what we're doing," Jentleson said. "People support this war because they see us restraining an aggressor. But when your strategy involves taking civilian casualties, that is very different."

Those questions will be asked more often abroad than in the United States, according to Jentleson. "The effect of civilian casualties will be more international than domestic," he said. "It is a problem in claiming moral legitimacy for our cause. . . . Indiscriminate casualties would feed into the radical Arab cause."