Obama made a strong argument for U.S. military intervention in Syria then backed away from it abruptly, Card said.
"I thought he made a very good case that Bashar Assad is a bad guy doing bad things and that the world should be outraged," he said. "But then he said I'm so outraged that I'm going to ask the world to step back for a little while and postpone the vote and we'll see if we can do something over the next period of time."
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Though Card said he did not see an imminent danger to the U.S. from Syria, he warned that this period of time for negotiations could be drawn out indefinitely.
"The truth is the timeline for negotiating, finding chemical weapons is going to be very long," he said. "I think he [Obama] gave Bashar Assad a pass."
As Bush chief of staff, Card broke the news of the Sept. 11 terrorist attack to the president from a second-grade classroom in Sarasota, Fla.
"I passed on two facts, one editorial comment, and I said a second plane hit the second tower, America is under attack," he recalled. "As soon as I heard about the second plane crashing into the World Trade Center, I knew that it wasn't a coincidence. I knew that it was a terrorist attack."
Though the moment remains clear in his recollection, Card said many have forgotten that the War on Terror continues.
(Read more: 12 years later, nation pauses to remember 9/11)
"The War on Terror was declared that day by the terrorists, and I think the War on Terror is still going on," he said. "Unfortunately I'm not sure that people in America are acknowledging that we are still in a war."
Card said the imminence of a threat from Syria is lower than the terrorist threats he faced from al-Qaeda and Saddam Hussein in the Bush administration, but said the situation with Assad has been magnified by President Obama's lack of leadership.
"Quite frankly, I think President Obama has exacerbated that problem because he has allowed others to take leadership roles."
--By CNBC Associate Producer Elizabeth Schulze. Follow her on Twitter