For most of the Bush administration, the war in Afghanistan was something of a political and media sideshow. Iraq was President Bush's albatross, but Afghanistan was the "good war": broad popular support, lower troop levels, fewer casualties -- and far less media coverage. But as President Obama takes ownership of Afghanistan and the war emerges from the shadow of Iraq in the media, the public relations picture isn't pretty.

Obama looks likely to increase troop levels to some degree, and a plurality of voters in a Quinnipiac University poll released Wednesday say they would support that move. So far, so good. But just what are those troops headed to the "graveyard of empires" to do?

Obama has made establishing a stable democracy a cornerstone of his Afghanistan policy. He's doubled spending on civilian governance and development to $200 million a month, and he's rejected Vice President Joe Biden's recent proposal to maintain current troop levels and focus on anti-terrorism raids on the Pakistani border.

But the American public has little interest in rebuilding Afghan society. Sixty-five percent of voters in the Quinnipiac poll think the primary U.S. role should be combating terrorism, while just 21 percent favor focusing on "building a stable democratic government." Respondents expect any nation-building efforts to fail, by a 3-1 margin. Obama has public support for troop increases, but for reasons different than his own.

It's fair to ask how terrorism in Afghanistan might be reduced without a stable democratic government; but the poll also shows that the public's grasp of the war is getting shaky. Eight years after the war began, a staggering 33 percent of Americans don't know why the U.S. invaded Afghanistan in the first place. And it's not as if Quinnipiac was asking for a term paper -- the pollsters accepted any answer that included any of six key words: "9/11," "al Qaeda," "Taliban," "Twin Towers," "Osama bin Laden" or "terrorists." Democrats fared the worst, with 42 percent unable to recall how the war started.

The public's ignorance isn't translating into deference on policy: 65 percent know the conflict's roots, but 86 percent have strong ideas about what our focus should be. Worse for the White House, voters place far more trust in the military to make decisions regarding troop levels (81-15 percent support) than in Obama (55-38 percent). That means that despite breaking historical protocol, Gen. Stanley McChrystal may have a powerful ally in the public if he decides to go rogue again and make policy recommendations, as he did last weekend.