In mid-March, when Gen. David Petraeus returned from Kabul to testify before Congress, an amazing thing happened. The media hardly paid any attention.

With revolutions popping up all over the Middle East, and the United States newly embroiled in Libya, the conflict in Afghanistan has vanished from the news pages. The Afghan war has become the forgotten war.

When reminded of it by pollsters, nearly two-thirds of Americans say the war is not worth fighting, and many of the war’s onetime supporters have become doubters. Yet no one has figured out a formula to extricate most or all of the 100,000 or so U.S. troops that does not risk plunging the country back into chaos.

So it’s not surprising we’re hearing talk again of pursuing talks with the Taliban to achieve a political solution to the Afghan conflict. A report on how to jump-start such talks was just released by the Century Foundation, based on a nine-month study led by former U.S. diplomat extraordinaire Tom Pickering and ex-U.N. envoy Lakhdar Brahimi, who helped produce and implement the Bonn peace accords at the end of the 2001 Afghan war.

Brahimi says there are prospects for peace talks that didn’t exist before.

The Taliban has been under heavy pressure in southern Afghanistan because of last year’s surge of U.S. troops and a campaign by U.S. Special Forces to target Taliban commanders. News reports indicate that they have also been beset by a wave of killings, arrests, and internal disputes in their haven in Pakistan.

“In 2006-2007 the Taliban were doing extremely well and were convinced they didn’t need to negotiate,” Brahimi said at a small dinner in Washington last week, where the report was introduced. “What has happened since is leading them to think it is not going to be that easy and perhaps it is better to negotiate a compromise.

“We think the Taliban may be interested in exploring negotiations, not more than that,” he added.

The task force has recommended appointing an “internationally designated facilitator” to explore if such talks are possible. Who would appoint such a person is left vague — maybe the United Nations.

It’s clear that Brahimi wants the job. It’s also clear that the current U.N. envoy in Afghanistan, the very capable Stefan de Mistura, does not want to be bypassed. Nor are U.S. officials — or Gen. Petraeus — likely to endorse handing off this role to an independent outsider.

The public U.S. position has been that any talks with the Taliban should be handled by Afghan President Hamid Karzai. A senior coalition official in Kabul told me via e-mail: “All here would welcome substantive talks, led by the Afghan High Peace Council (a not-very promising body created by Karzai) and the Afghan government.”

But the official added something more interesting: “There appears to be somewhat greater likelihood of such talks now than, say, last fall.”

Indeed, the late U.S. special envoy to Afghanistan, Richard Holbrooke, had been pushing for such talks, no doubt in hopes that he could repeat his success in brokering the Dayton peace accords in the Balkans. And there have been recent reports of secret exploratory talks between administration officials and senior Afghan Taliban leaders.

Such feelers have failed before. Afghanistan’s neighbors, especially Pakistan (whose security services want to control any talks with the Taliban) may undercut them. But there is a bigger strategic question beyond who should facilitate such talks: Does the concept really offer any hope of ending the Afghan war?

This question is often finessed by those who seek talks, out of a desperate desire to break the Afghan impasse. Despite the military gains by Petraeus in “clearing” Taliban from the south, the other pillars of his strategy — hold, build, and transfer to Afghans — are shaky.

The corrupt Karzai government often undercuts progress at provincial and local levels. This makes it hard to build up cleared areas; moreover, Afghan security forces are far from ready to take over. And Obama has pledged to withdraw all combat forces by 2014, starting in 2011.

Yet a deal with the Taliban offers no guarantees of peace. In many conversations with Afghans over the past two years, in villages and towns in several provinces, I heard the same complaint: The elders wanted neither the Taliban nor the Karzai government. They were fed up with government corruption — which, they said, drove youths into Taliban ranks. But they didn’t want a return of cruel Taliban rule; polls consistently bear this out.

So any exploratory talks — no matter the interlocutor — must concentrate on two core issues.

First, they need to figure out who really speaks for the Taliban, especially Mullah Mohammed Omar’s Quetta Shura. Everyone recalls the supposed Taliban leader who was brought to meet Karzai late last year, with the help of British security agents, and was given large sums of cash. He turned out to be an imposter. Until the Taliban appoints a political leadership, talks with individuals may not mean much.

And, if those leaders become known, the interlocutor needs to figure out whether they still dream of an emirate based on their harsh version of sharia, either in all of Afghanistan or in Pashtun provinces in the east and south. Or is that leadership, in part or whole, ready to listen to what Afghans want?

If Karzai makes a deal with some Taliban leaders that alienates large swaths of the Afghan people there will be no peace. There will be a civil war that spills over into nuclear-armed Pakistan next door.

As much as we want to leave — and forget — Afghanistan, talks with the Taliban are no silver bullet. It makes sense to send a facilitator to explore the Taliban mind-set, but talks won’t work unless that mind-set has changed.