Petraeus: How will he be remembered?

(CBS News) When the news broke of CIA Director David Petraeus submitting his resignation to President Obama over an extramarital affair, there was shock on both sides of the political aisle.

Petraeus' high-profile career has made him one of the most well-known generals of his generation, winning him widespread praise. But now there are questions as to what effect his departure will have on his legacy.

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Washington Post columnist David Ignatius spoke to Anthony Mason and Rebecca Jarvis about how Gen. Petraeus gained his stellar reputation through his 37-year military career.

"When he was named commander in Iraq in 2007, even the U.S. military had essentially given up on the war," Ignatius said. "During the next two years, he would come back to Congress -- you remember that image of that general with all those medals -- selling the country that the war in Iraq was turning around. We could move U.S. troops in a more honorable way. It was a great achievement."

Before serving as commander of the International Security Assistance Force, and as the commander of U.S. forces in Afghanistan, Petraeus' ambitious counterinsurgency strategy was credited with turning around the Iraq War. In a statement about the general, President Obama said Petraeus helped the military "adapt to new challenges" and helped the nation put the wars in Iraq and Afghanistan "on a path to a responsible end."

Then, in 2011, Petraeus was tapped as the Director of the Central Intelligence Agency, where he had to adapt to a very different culture than he was used to in the military.

"I think it was difficult in large part because of the nature of the place," Ignatius said. "Petraeus, like many other military officers, is a control guy. He is used to people saluting and doing what he told them to do when he gives an order. And he was in a very different kind of bureaucracy."

Petraeus was scheduled to testify before Congress about the attack on the U.S. Consulate there that killed four Americans, including Ambassador Chris Stevens. Ignatius was asked if Petraeus' resignation could tarnish testimony coming from the CIA on the matter.

"I don't know that it would tarnish the testimony," he said. "Petraeus, because he's so visible -- he's one of the most famous faces in America -- would have been a lightning rod for critics of the agency's performance."

Petraeus will be replaced by the acting director, Michael Morell, who oversaw the agency during the last gap between directors.

"I think the story they will tell is one of some misjudgments, and I think Congressional critics rightly will jump on them for those misjudgments about relying on local Libyan militias," Ignatius said of Benghazi. "A painful hearing for people at the CIA, but I wouldn't think it would generate as many headlines with Petraeus gone."

To watch the full interview with Washington Post columnist David Ignatius, click on the video above.

To watch Jeff Glor's "Author Talk" interview with Petraeus biographer Paula Broadwell, who has been linked to the CIA Director's resignation, click on the video below.