Gen. John Allen, the former commander of U.S. troops in Afghanistan, recommended between 6,000 and 15,000 troops. But that figure was lowered to a range between 2,500 and 9,000, according to a defense official.
There might not be any U.S. troops at all if the United States cannot come to an agreement over immunity with Afghanistan. There was no American presence in Iraq at the end of that war because the Iraqi government refused to extend legal protections to U.S. troops.
Karzai, who's in favor of a residual force, said he would put the immunity decision in the hands of Afghan elders, and he expressed confidence that he could persuade the elders to see things his way.
Leaving no U.S. troops at all would be a major misstep, said Peter Bergen, CNN's national security analyst. He said the U.S. has abandoned Afghanistan already, in 1989, and the decision left America with little understanding of the power vacuum that led to the Taliban's rise in the first place.
"The current public discussion of zero U.S. troop presence in Afghanistan ... will encourage those hardliner elements of the Taliban who have no interest in a negotiated settlement and believe they can simply wait the Americans out," Bergen wrote in an op-ed for CNN.com. "It also discourages the many millions of Afghans who see a longtime U.S. presence as the best guarantor that the Taliban won't come back in any meaningful way."
3. What's at stake?
The main fear among the Afghan people is that the country could revert to another civil war once the United States withdraws its combat troops. The Taliban are still "resilient and determined," according to a recent Pentagon report, and insurgents continue to carry out attacks and pose a major security threat.
"Some people we've spoken to sort of take it for granted that there's going to be a civil war when the United States leaves," said CNN's Erin Burnett on a recent trip to Afghanistan. "It happened before when the Soviet Union left (in 1989)."
For all the violence Afghanistan has seen in the past decade, it has also seen major advancements in human rights and quality of life.
"During the Taliban, basically there were thousands of girls going to school in Afghanistan. Now you have millions of girls going to school," Burnett said. "So there's been real progress on women's rights. Obviously there remain a lot of problems -- honor killings, forced marriages, domestic violence -- but there has been real progress."
Retired Army Gen. Stanley McChrystal, once America's top commander in Afghanistan, said the Afghan people are "terrified."
"They're terrified because they think they have something to lose," McChrystal said. "There has been progress made. There is a better life. There are girls in school. There are things that are better than they were and opportunities potentially ahead.
"But they're afraid that if we completely abandon them in 2014, as they perceive we did in 1989, (things) would all go back."
And in Washington, there are worries that the wrong move could put the United States right back where it started, with nothing to show for a bloody conflict that started in 2001.
Chairman of the House Armed Services Committee, Rep. Buck McKeon, R-California, expressed concern last week that a hasty withdrawal could be "needlessly fraught with risk."
"Since the president took the commendable step of deploying a surge to Afghanistan in 2009, we have known that our hard-fought gains are fragile and reversible," McKeon said. "That isn't my assessment, but the consistent opinion of experts both military and civilian."
4. Who will lead after Karzai?
Afghanistan's only president of this century won't be in charge for much longer.
Elections are scheduled for April 2014, and Karzai has reached the term limit set by his country's constitution. He told Amanpour it's "absolutely time to go."
"A new president will come to this country. A new government will come to this country. And I'll be a happily retired civil servant," he said.