"Mr. Secretary, is there a deadline or is there not?" CBS News Senior Washington Correspondent Bob Schieffer asked Gates.
"There isn't a deadline," Gates said. "What we have is a specific date which we will begin transferring responsibility for security district by district, province by province in Afghanistan to the Afghans."
Schieffer's full interview with Gates and Secretary of State Hillary Clinton is scheduled to be broadcast Sunday on "Face the Nation."
In his speech Tuesday, Mr. Obama said he will send an additional 30,000 troops to Afghanistan. The president said he intends to pull those troops back from Afghanistan after 18 months.
Secretary of State Hillary Clinton said of the July 2011 date, "it's not an arbitrary time. It is an assessment based on what we see happening that yes, we will be able to transfer responsibility and that will very likely mean some troops can come home."
Republicans have mobilized against the prospect of a deadline for withdrawal including Senator John McCain, R-Ariz., who told CBS "Evening News" Anchor Katie Couric July 2011 was "an arbitrary date for withdrawal."
Gates explained that the 18-month timeline is meant to convince the Afghanistan government that U.S. support is strong but not endless.
"It's an effort to try to let the Afghans know that while we intend to have a relationship and support them for a long time the nature of that relationship is going to begin to change in July of 2011," Gates said. "As the security component comes down, the economic, development and political relationship will become a bigger part of the relationship. We are not going to abandon Afghanistan like we did in 1989, but the nature of the relationship will change."