U.S. and Afghan politicians are in the middle of a heated debate over whether a small American and NATO force will remain in Afghanistan at the end of next year.

But what's a political and strategic question at the negotiating table is an emotional question at bases around Afghanistan, where soldiers watch the discussions with one eye on their sacrifices over the past 12 years and the other on the American withdrawal from Vietnam four decades ago.

In short, they don't want to go home without the win.

After repeated combat tours, an untold number of divorces and nearly 2,300 U.S. dead, American servicemen want their losses in Afghanistan to have been worth it. For many of them, that means keeping a residual force here to help the Afghans fend off a resurgent Taliban.

The sense is especially sharp among elite special-operations troops. They were the first U.S. forces on the ground in Afghanistan in 2001, fighting alongside Northern Alliance rebels to oust the Taliban regime that had sheltered Osama bin Laden and al Qaeda. And they are the ones likely to form the backbone of any force the U.S. would leave in place to buttress the Afghan military and government after the bulk of coalition forces withdraw by the end of next year.

"There's some ownership of this," says Maj. Gen. Austin Scott Miller, who has spent three years in Afghanistan since 2001 and now commands allied special-operating forces there. "There are people who have been here since the beginning."

The U.S. military would like to keep close to 9,000 American troops in Afghanistan after 2014, with a smaller contribution from allied nations, according to a senior Obama administration official. That force would likely be heavy with Army Green Berets, Marine Corps special-operations troops, Navy SEALs and other specialized units, which work closely with select Afghan forces.

U.S. Secretary of State John Kerry and Afghan President Hamid Karzai made progress this month in hammering out an accord that would allow a continued American and NATO military presence beyond 2014. But the deal is still hung up on several points, including the touchy question of whether U.S. troops would be subject to Afghan law. Mr. Karzai has said that he won't approve immunity for foreign troops unless it is approved by a gathering of traditional Afghan leaders, or Loya Jirga. A similar immunity dispute sank U.S. efforts to leave a rump force in Iraq in 2011.

"We'd like to stay in the long term, and our [Afghan National Security Force] partners have indicated they want us to stay," says Gen. Miller. "The relationships between us run deep after 12 years."

The ignominious U.S. exit from Vietnam—helicopters lifting the last Americans and desperate Vietnamese from a Saigon rooftop—isn't far from the minds of U.S. troops as American participation winds down in Afghanistan. A more personal fear, perhaps, is becoming like the Vietnam veterans of popular imagination, bitter over losing their friends and their youth in a failed effort to prevent a Communist takeover of the country's south.

Col. Pat Roberson, commander of 3rd Special Forces Group, whose men operate in the hotly contested Helmand province, is reading "A Better War," a history of American operations in the last half of the Vietnam War. The author, historian and Vietnam veteran Lewis Sorley, argues that after 1968, Gen. Creighton Abrams turned the military situation in Vietnam around by upgrading the South Vietnamese army and focusing on smaller operations to protect the population from the Viet Cong, rather than major battles with large North Vietnamese and insurgent units. It is an approach echoed in the U.S. transition strategy in Afghanistan today.

The book portrays the 1973 peace accord and the American troop withdrawal as a political sellout at a time when the U.S. military and its Vietnamese allies were finally making progress.

Col. Roberson is careful to say that he doesn't see the book as an exact analogy for the situation in Afghanistan. But, with his men racing to prepare Afghan forces to fight on alone, "there are parallels," he says. "You're looking at history as kind of a guide to the future."

What's a win? "Really it's a successful transition of power," says Col. Roberson. "For me, it's getting these guys set up for success as much as possible."

It isn't that U.S. commanders express pessimism about the outcome in Afghanistan; Gen. Miller and Col. Roberson say that Afghan troops are better able than ever before to take on the insurgents. Nationwide, they often operate virtually independent of coalition support, although Afghan military casualties are soaring as a result.

Still, there's pervasive sense among elite U.S. troops that the end of next year is too early to go home. In Helmand's Kajaki district, where the U.S. built a hydroelectric dam 60 years ago, one Marine staff sergeant reflected recently on his third Afghan tour in four years. He missed his daughter's birth two months ago; he was on emergency leave, rushing home from the battlefield, when his wife went into labor. He has lost two very close friends in Afghanistan. He escorted one friend's body home. Despite the heavy price—or perhaps because of it—he says: "I think we need to have the conviction as special-operating forces to finish this fight."

"I feel like we've made it to the 1-yard line," says the staff sergeant. "And if we can just see it through to the goal line…."

In the headquarters building at a major base, Lt. Col. Joe McGraw, commander of 2nd Battalion, 1st Special Forces Group, often finds himself walking a hallway lined with the photos of young Marines, soldiers, sailors and airmen killed in Helmand province over the past 12 years. "You walk down that hallway and realize it's not dozens—it's hundreds and hundreds," he says.

The price paid in "blood and flesh" makes it hard for Lt. Col. McGraw to swallow the idea of leaving too early. "Nobody comes over here looking to lose," he says.

Still, the elite troops recognize that the very concept of victory is elusive in Afghanistan, where religion, politics, corruption and crime mix together to muddy the definition of friend and foe. No matter how long U.S. forces stay, they say, there is unlikely to be a final battle or surrender.

One Marine major—who has missed half of the Christmases in his son's seven years—says, "For something like this, winning and losing is too black and white." Afghanistan, he predicts, will long have pockets of violence. But, he says, however the next few years play out, the war has already achieved its major goal.

"I don't think there's an al Qaeda-type element who will ever come back into power and threaten my country and my family," says the major. "That's victory to me."