Petraeus assumed the post of top commander in Iraq in February, and said while Americans work to turn over more security to the Iraqis, the efforts to train a local military is hampered by their own troop losses and equipment shortages.
There is also the issue of loyalty, as some Iraqis have a greater sense of attachment to their ethnicity than Iraq as a nation. Petraeus said "it is changing slowly" but "there's no question, but that large segments of the population do have that kind of loyalty."
For now, he said the U.S. troops are critical to provide support for their Iraqi counterparts and to take an active role in the fight against the insurgents.
"If we were not helping go after the insurgents, the militia extremists, the terrorists, but were literally just supporting the Iraqis in that role, the operations would not be as effective," he said.
He said the gains against al Qaeda have been both facilitated and led by U.S. troops. "Especially when it comes to our most special special operations forces, which are drawing on levels of intelligence capability and just sheer combat skill and capability and communications and so forth that the Iraqis just do not have."
The troops also face an influx of what Petraeus called "lethal aid" from Iran to the insurgents. Given the range of challenges to progress, Gibson asked Petraeus what he envisions during his most optimistic moments.
"First of all, I have tried to shut out optimistic and pessimistic moments, candidly, and just have realistic moments. And what I see in those moments is a very tough, very hard effort ahead," he said. "And I'm not going to sugarcoat that. And the ambassador [Ryan Crocker] has sought to say that this is hard. He always uses that word."
Still, Petraeus maintains this is a critical mission that is worth the sacrifice of American lives. "If I didn't think that, I wouldn't be doing this job. We have enormous interests at stake in Iraq, and it is hugely important that we help Iraq get it right."