"A lot of the other NATO allies have fallen short of their commitment and we are going to put maximum pressure on them," Levin told CBS News Chief Washington Correspondent and "Face the Nation" Anchor Bob Schieffer, noting the importance of not allowing the Afghan-Pakistan border to become a safe haven for terrorists.
Republican Sen. Lindsey Graham admitted "I am one Republican that would support more troops in Afghanistan ... I would be shocked if more troops are not requested by our commanders."
The South Carolinian said he disagreed with President Obama's assertion during last year's presidential campaign that Afghanistan was the central battle in the War on Terror. Now, he said, that Iraq is more stable he agrees with the president's assessment.
Graham, who also serves on the Armed Services Committee, said, "My message to my Democratic colleagues is: We made mistakes in Iraq, let's not Rumsfeld Afghanistan."
"Let's not do this thing on the cheap," he said.
By "Rumsfeld[ing]," Graham explained that he meant in Iraq there were not enough American troops on the ground to control the population. "Don't resist the fact that we are going to need more [troops]."
Levin said that in addition to putting pressure on NATO allies to send more troops, the U.S. will also have to also better train and increase the already determined Afghanistan army.
He said the war in Afghanistan is going to take "a lot more of most things" but at this point the U.S. should not agree to providing more troops.
Levin also agreed with Gen. Jim Jones, Mr. Obama's national security adviser, that the closing of Guantanamo Bay could be done by the administration's deadline of early next year.