Public support for the war with Iraq remains strong despite more grim news from the front, diminished expectations that the conflict will be brief and relatively bloodless, and the widespread belief at home that the looming battle for Baghdad will be particularly difficult, according to a Washington Post-ABC News poll conducted Sunday night.

The survey found that 54 percent of the country now believes the United States and its allies will sustain "significant" casualties in the war, up from 37 percent on Thursday, the day after President Bush declared war on Iraq and allied forces launched a limited airstrike on Baghdad.

Many Americans also expect a somewhat longer war than they did a few days ago. Nearly half -- 45 percent -- now expect the war to last months rather than days or weeks, up from 37 percent on Thursday. Eight in 10 expect a difficult fight to control Baghdad, a view shared by equally large majorities of those who support the war and those who oppose it.

"We think this is tough now, wait 'til we get to Baghdad," said Mike Shipe, 28, a mechanic who lives in Columbus, Ohio. "That's where they're hunkered down. That's where the real fighting is going to be. . . . It's going to be a doozy over there."

Yet these somber assessments have not diminished overall support for the war effort or favorable views of Bush's handling of it, both of which have risen in recent days.

More than seven in 10 Americans currently back the president's decision to go to war, unchanged from the start of the campaign. Seven in 10 (71 percent) approve of the way he is handling the situation in Iraq, up 6 percentage points from three days ago and higher than at any time in the past seven months. Bush's overall job approval rating was unchanged, at 68 percent.

The survey found that eight in 10 Americans believe the campaign is going well, although only about a third said it was going "very well" for the United States. Even opponents acknowledged that the invasion seemed to be accomplishing its goals: 63 percent of those against the war said it was going well for allied forces.

Overall, two in three said the war to oust Iraqi President Saddam Hussein and rid Iraq of weapons of mass destruction was progressing about as they had expected. More Americans (19 percent) said the conflict was going better than they anticipated than those who thought it was going worse (10 percent).

Those evaluations are somewhat less positive than those in surveys conducted in the first days of the Persian Gulf War in 1991, when 39 percent thought the conflict was going better than they thought it would.

"Up until today [Sunday], I think it had gone very well for us," said Sheryl Leach, 63, a retired government worker who lives in Mooreland, Okla. "I think today is a day we had to expect was going to come along. I don't think anyone expected we could walk right in there with no opposition whatsoever."

Daphne Nugent, 40, who works for a health care company and lives in New York City, disagrees. "I didn't expect there to be this much trouble," she said. "And I'm a little upset by what I'm hearing in terms of the casualties and the prisoners of war. . . . I thought it would end pretty easily and quickly -- the war part of it anyway, not the occupation part."

Despite reports Sunday of fierce fighting and growing allied losses, half of those interviewed said the number of U.S. military casualties so far was about what they expected. One in four said casualties were greater than they initially thought they would be, and an equal proportion said the losses were smaller than they had anticipated.

Republicans remain nearly unanimous in their support for the war. While majorities of Democrats and independents also expressed support, large minorities of each group remain opposed.

The survey found 95 percent of Republicans backing the war with Iraq, including 82 percent who said they "strongly support" the invasion. In contrast, about six in 10 Democrats and political independents currently support the war, with roughly four in 10 opposing it.

There is a gender gap in terms of support for the war, although not a large one. The Post-ABC poll found that 78 percent of men supported it, compared with 66 percent of women.

A total of 580 randomly selected Americans were interviewed Sunday. The margin of sampling error for the overall results is plus or minus 4 percentage points.

The survey found that protests at home and abroad have done little to affect public opinion on the war. If anything, they have deepened support among those who already favored using military force against Iraq.

Seven in 10 said the antiwar rallies have not changed their opinion on the conflict. One in five said the protests have made them more likely to back the war, while 7 percent said it has increased their opposition to the conflict.

Six in 10 agreed that the demonstrations were a sign of a healthy democracy, while fewer than four in 10 said opponents should not demonstrate against the war because it was better for the country to appear united. Only one in six said such protests should not be permitted.

"I have a hard time seeing people protest the war," said Ted Stahl, 40, a metalworker who lives in Jasper, Ga. "I don't have problems with people having the right to voice opinions. But people live in the U.S., a great nation of freedom, and they mock our nation's freedom and our government."

Overall the survey suggests that few Americans have attended antiwar demonstrations (2 percent) or rallies in support of the war effort (1 percent).