It's not every day that an American officer goes on television to emphasize a global crisis can't be fixed by the US military. But that's exactly what Gen. Ray Odierno just did on CBS This Morning.

The US Army chief of staff, who spent over six years in Iraq, including as the head of all foreign forces from 2008-2010, went to great lengths to emphasize that US military efforts can't be decisive in the war against the so-called Islamic state under current conditions.

Yesterday, President Obama said 450 more US soldiers will be deployed under an expanded training mission in Iraq, with a focus on arming and training Sunni Arabs, who feel excluded and oppressed under a Shiite-dominated government. But Odierno said that even sending 150,000 US troops to the country - roughly the number of soldiers during the 2007-08 "surge" that helped tamp down mass killings – would be wasted without a major reorientation by Iraq's Shiite leaders.

"You've got to understand why this is happening," Odierno told CBS. "My thought is we had this in a good place three or four years ago and Iraq was safe, the economy was growing we turned it over to the Iraqi government. I believe it's because the Iraqi government has not been able to bring all the different groups together. Until you solve that problem in my mind it doesn't matter how many people you put on the ground."

Having laid out this political analysis, he turned to a hypothetical deployment of US combat troops. "My worry is, could I put 150,000 soldiers on the ground and defeat ISIS? Yes. But then what?... It would go right back to where we are, a year later it would be right back where we are today. So I believe before we even consider anything like that we need to solve the political problem."

Of course, US political influence in Iraq has been on the wane since Shiite Islamist parties stormed to electoral victory in 2005 and has probably never been lower than now. Iran's influence has meanwhile been on the rise, thanks in part to its close ties to the Shiite militants and dissidents who lived in exile during Saddam Hussein's years in power and returned home to lead the country after the US-led 2003 invasion.

Odierno also said that regional support is necessary to defeat IS and restore Iraqi stability, but acknowledged the extensive roadblocks in the way:

In order to solve this problem you need the Arab communities to solve this problem. The United States can not solve this problem by itself. We need the Arabs to step up, we need them to understand we have extremism here and they have to help us, to include the Iraqis... Throughout the Middle East there is this underlying Sunni Shia issue, Iran Saudi Arabia, Sunni Shia, that's playing out and that's what's making it more difficult for us and for anybody else to help them in order to defeat this threat.

The rivalry is at least as much cultural as religious: Persian Iran is vying with Saudi Arabia for regional influence. Since Iran's 1979 Islamic Revolution, Saddam's Iraq served as a major check on Iran's regional influence, the bloody war in the 1980s between the two countries claiming hundreds of thousands of lives on both sides.

Odierno also called for a complete restructuring of Iraq's military, which in recent years has come to look more like a Shiite jobs program than a national force dedicated to the equal protection of all Iraqis. Building the Iraqi army was a process Odierno was intimately involved in. And he blamed Iraq's Shiite political leaders for what it's become.

"I think over the last two to three years the (military) leadership was purged, the leadership we trained was purged," Odierno said. "I think they have to improve their leaders... we need to see the right leaders in place that are loyal to fighting this fight not loyal to a very specific individual in the government."

The answer Odierno provides to the problem is a simple one. "What we need is a totally integrated army of Sunni, Shia and Kurdish fighters that are there for Iraq and that are willing to fight for Iraq.... once that's done we can train them and we can help them. But until they can put together an army that represents everybody I think it's going to be a struggle. The reason we're opening this new site is because we're trying to reach out to Sunni fighters and have them come in and join."

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How could that be accomplished? Again, politics is the key:

We need the government to really start to reform itself.... Prime Minister Abadi has said all the right things. I believe he's trying to do the right things. I think there's still a lot undercurrents within the Iraqi government that's making it very difficult for him to do that... there's a lot of behind the scenes things going on that are making if difficult for him in order to do the reforms that are necessary i.e. reach out to the Sunnis, bring them in as part of the government, make an oil deal with the Kurds, which he has done, and follow through on that.

There's been a decade of Iraqi leaders saying the right things and doing otherwise. Perhaps things will change now. But that's out of the hands of General Odierno and the Pentagon.