But The Early Show co-anchor Harry Smith, who'll be there all week, got a special tour of one small city, and he got a firsthand look at how U.S. troops are faring.
"We were looking for a little optimism, and a little progress, and we found it, in a place called Saba Bor," Smith says.
It's a short ride in a Black Hawk helicopter from the secure "green zone" in downtown Baghdad to Taji, an army command center northwest of the capital.
"It's funny: I feel more confident flying with these guys in a combat zone then I do sometimes flying in the states," Smith says.
Soon, Smith was going over emergency procedures as he and some soldiers headed to Saba al Bor, which Smith called "a work in progress."
He was with Col. David Thomson's outfit, from the 4th Infantry Division.
Looking for some reassurance, Smith asks Thomson: "Where we're going, should it be smooth sailing?"
"Harry, there's no guarantees in this business," Thomson says, "but, I'll do my best. It should be fairly smooth. We've had some enemy activity out there, but I think it should be relatively quiet. We'll see."
"We headed to town in our armored humvee, gunner up top, at the ready," Smith says. "Local traffic pulled over. We had our eyes peeled for IEDs (improvised explosive devices)."
At the local command center, Lt. Tyrek Swaby tells Smith that Saba al Bor is home to 60,000 people — half Shiite, half Sunni — and it's never been friendly territory.
"When we first came here in January," Swaby says, "you could see the fear in people's eyes, fear of the unknown. … But now, the attacks have dropped down significantly."
And the enlisted man sees it the same way.
"When we got here," says Pfc. Joseph Higgins, "the reaction of the people was — you'd ask how they liked Americans, and they … might say anything to you, or might not even talk to you, or they'd say, 'We don't really like Americans.' But now we're doing a lot for these people and they say, 'Yeah, Americans are good. You see it especially in children."
"Patrol starts in a sparsely populated part of town and works its way to the city center," Smith says. "These guys are armed to the teeth, but the most important thing they carry is — candy.
"It's an image we haven't seen much in three years: friendly faces, people eager to chat up an officer, even try out their English!"
One teen even tried to say his name was Bush.