"This was the night when Barack Obama that took full ownership of the war in Afghanistan," he said. "We're going to have 100,000 troops there, and more than half of them will have been sent there by the President."
In the speech, President Obama announced that 30,000 additional troops would be sent to Afghanistan.
The "Face the Nation" host also questioned Mr. Obama's strategy of setting a timetable for the troops to come home.
"How do you on the one hand say, 'we need to send these troops over there, it's critical, this is in our national security interest to do this'" Schieffer said, "but then say, 'but we're only going to keep 'em there for 18 months.'"
"I just don't understand the logic of how that works," Schieffer added. "How you can set a deadline on what you're going to do, and you know, this is not a football game where there's a clock where the time runs out."
More Coverage of Obama's Speech on Afghanistan:
Marc Ambinder's Analysis: Obama Taking Big Risk
Who Offers the Better Deal in Afghanistan?
Liberal Lawmakers, Activists Chastise Afghanistan Troop Increase
Polling Analysis: Afghanistan 2009 Vs. Iraq 2007
CBSNews.com Special Report: Afghanistan