The poll also follows a number of high-profile killings of American troops by their Afghan partners — a trend that the top American commander in Afghanistan suggested on Monday was likely to continue.

“It is a characteristic of this kind of warfare,” Gen. John R. Allen, the commander of NATO forces in Afghanistan, told reporters at a Pentagon news conference. He said that in a counterinsurgency conflict like the one in Afghanistan, where American forces are fighting insurgents while training Afghan security forces, “the enemy’s going to do all that they can to disrupt both the counterinsurgency operation, but also disrupt the integrity of the indigenous forces.” American commanders say that the Taliban have in some cases infiltrated Afghan security forces to attack Americans, but that most cases are a result of personal disputes between Afghans and their American trainers.

In follow-up interviews, a number of poll respondents said they were weary after more than a decade of war in Afghanistan, and impatient with the slow progress of Afghan security forces. “I think we should speed up when we’re bringing our troops home,” said Melisa Clemmons, 52, a Republican and a coordinator for a wireless carrier system from Summerville, S.C. “If we’ve been there as many years as we’ve been there, what’s another two years going to get us?” she asked, adding, “These Afghanistan people are turning around and shooting our people. Why is it taking this long for the Afghan troops to be policing themselves?”

Image Credit... The New York Times

Paul Fisher, 53, a Republican from Grapevine, Tex., who works in the pharmaceutical business, said the United States should no longer be involved in the war, although he opposed setting a specific timetable. “After a while enough is enough, and we need to get out and move on and let Afghanistan stand on its own merits,” he said.

Peter Feaver of Duke University, who has long studied public opinion about war and worked in the administration of President George W. Bush, said that in his view there would be more support for the war if President Obama talked more about it. “He has not expended much political capital in defense of his policy,” Mr. Feaver said. “He doesn’t talk about winning in 2014; he talks about leaving in 2014. In a sense that protects him from an attack from the left, but I would think it has the pernicious effect of softening political support for the existing policy.”

The drop in support for the war among Republican poll respondents mirrors reassessments of the war among the party’s presidential candidates, traditionally more hawkish than Democrats. Newt Gingrich declared this month that it was time to leave Afghanistan, while Rick Santorum said that one option would be to withdraw even earlier than the Obama administration’s timeline. Mitt Romney has been more equivocal, although he said last summer that it was “time for us to bring our troops home as soon as we possibly can, as soon as our generals think it’s O.K.”