The stubborn war in Afghanistan, which has spanned a decade and cost more than 2,000 American lives, has now faded to one key question: How many U.S. troops will remain after 2014?

This is the issue that will likely occupy President Barack Obama and Afghan President Hamid Karzai when they meet at the White House on Friday. Officials are already batting numbers about, ranging from zero to 20,000.

But how many Americans are still paying attention?

For many voters, and those they elect, the war is over. Only brief and irritating interruptions, like the scandal the led to the resignation of CIA director and retired General David Petraeus, serve to remind the public that the United States remains at war. In the presidential campaign, candidates in both parties mentioned the war only in passing. GOP nominee Mitt Romney didn’t even say “Afghanistan” in his convention acceptance speech, while Obama and Vice President Joe Biden referred to the war only to discuss its “responsible end.”

For those who served in Afghanistan on the diplomatic or military front and believe in continued U.S. engagement, the battle is now against an opponent for whom they have few weapons: U.S. public apathy.

And they are losing the fight.

For a long while now, the American public has stopped believing the war is worth its cost. Few in the Obama administration have mustered an argument that answers their concerns.

That has not escaped notice.

“We are now coming up to certain very critical decisions,” Ronald Neumann, former U.S. ambassador to Afghanistan, said recently at the Brookings Institution, “that will be made fairly soon, both about our presence in Afghanistan after 2014 and about the next year, what we will do in terms of troop levels. The fact is we have a policy. What we are not clear about is whether we’re serious about that policy ‑ and what the policy requires.”

Neumann noted, “We’re talking about leaving, so you’re having a debate about numbers which floats ethereally without being connected to missions.”

Yet talking about the mission – the “good war” whose eventual goal became “good enough” – is what most of Washington has avoided. By not discussing in depth the war and its objectives, the administration has allowed the American public to believe there is nothing to salvage in Afghanistan after a decade of battle.

This idea of Afghanistan as hopeless, says the celebrated diplomatic workhorse Ryan Crocker, who most recently served as ambassador to Afghanistan, should be questioned. Leaving Afghanistan with little financial, civilian or military support, he said, is a lethal recipe for history to repeat.

“I hear all too often,” Crocker told me recently at the Council on Foreign Relations, “ You know, ‘We’re tired of this;’ ‘It’s costing too much;’ ‘It’s taken too long.’ ‘You know, we got problems here, it’s time to pull the forces and let the Afghans do the best they can.’ Well, we tried that once, of course, after the expulsion of the Soviets. It did not work well.”

General Stanley McChrystal, who commanded U.S. forces in Afghanistan until a Rolling Stone article forced him into retirement, shares Crocker’s concerns about leaving Afghanistan on its own.

“We have an emotional responsibility” to Afghanistan, McChrystal said in a recent interview. “We created expectations after 2001 in people.”

Though McChrystal would not put a number to the ideal post-2014 troop level, he has argued that the U.S. must still fulfill its pledge to help train Afghan forces.

Crocker, now at Yale University, along with McChrystal, agreed.

“I hope that if the Afghans, in our current negotiations,” Crocker said, “do make requests for a post-2014 presence, that we very positively consider it. And I hope very, very much, that we not hack and slash the plans for a post-2014 civilian presence. As I am deeply afraid we are. Because if we’re not there to engage, we have no influence.”

That lack of influence does not matter to those who want out as soon as possible. They point to the costs of the Afghan war and say they are ready for those to end.

But Crocker and others say the bill for supporting the Afghan military is far more affordable than another war.

“We will wind up paying about $2.5 billion a year as our share of support for Afghan security forces totaling 230,000,” Crocker said. “That sounds like a lot of money ‑ until you consider that we’re paying about $110 billion a year now. So this is pretty cheap insurance.”

Whether that insurance will be sufficient to help Afghans protect their nation and avoid a descent into civil war remains in doubt. But as Obama and Karzai meet in Washington, the call for clarity on U.S. objectives and commitments has grown ever louder.

And those who have followed Afghanistan for decades say a little candor would be helpful, too.

“It does seem to me,” Neumann, the former U.S. ambassador, said, “that the greatest single contribution that America could make to having this thing come out a little better rather than a little worse is clarity about our own purpose. I can’t, sitting here, tell you whether I believe that this administration is actually committed to trying to make the Afghan army as good as it can be in the next two years or whether we’re simply trying to look for a decent interval while we dump that.

“If I can’t tell you,” he said, “it’s not surprising that Afghans can’t tell you.”

Neumann emphasized, “I bridle a little every time I hear the words … from certain higher levels that we are winding down the war ‑ because we are not winding down a damn thing.

“We’re winding down our participation in the war,” he continued. “That is extraordinarily different from winding down the war. And we should be clear about that.”

PHOTO (Top): Afghan President Hamid Karzai addresses soldiers and family members assigned to the 101st Airborne Division at Fort Campbell, May 14, 2010. REUTERS/Chad J. McNeeley/U.S. Army/Handout

PHOTO (Insert): Afghan President Hamid Karzai (R) pins on a medal for a newly graduated officer at the National Military Academy in Kabul March 22, 2011. REUTERS/Omar Sobhani