"This is going to be hard, Bob... I am under no illusions," he said. "If it was easy it would already have been completed."
The two spoke for an interview that will air in full on CBS' "Face The Nation" Sunday.
"We're going to have to go with a strategy that is focused, that is narrowly targeted on defeating al-Qaeda," the president said.
Added Mr. Obama: "We think that if you combine military, civilian, diplomatic, development approaches, if we are doing a much better job coordination with our allies, that we can be successful."
The president also told Schieffer that, during a meeting at the White House Friday, he asked bank CEOs to "show some restraint" in their spending - especially when the financial institutions in question are recieving federal aid.
Mr. Obama said he asked the bankers to "show that you get that this is a crisis and everybody has to make sacrifices" during the meeting. Schieffer asked him about the bankers' response to his appeal; Mr. Obama said they "agreed" and "recognized" the problem.
The president then said that when it comes to real results, "the proof of the pudding is in the eating."
Check your local listings to find out when and where "Face The Nation" will be airing in your area on Sunday, March 29.
Bob Schieffer gives CBS News anchor Katie Couric a preview: