Upon receiving the first reports that a U.S. Army staff sergeant allegedly had killed 16 Afghan civilians Sunday morning, Washington sprang into crisis mode. Top White House and Pentagon officials feared that the reaction in Afghanistan would dwarf the riots and retribution killings sparked by the burning of several Korans at a U.S. base three weeks earlier.

They braced for Afghan political leaders to make even more strident demands to reduce the number of foreign troops on Afghan soil. Some civilian members of President Obama’s national security staff also viewed the killings as a siren call for a more rapid withdrawal of U.S. forces.

“This has the potential,” one administration official said, “to become a game-changing moment.”

The initial reaction, however, suggests that this crisis may well hew to the arc of other moments of brinkmanship in the U.S.- Afghan relationship: claims of irreparable damage and demands for profound change, followed by a grudging recognition in both capitals that the two governments have more reasons than not to stick with their previously agreed-upon strategy of fighting the Taliban, training the Afghan security forces and creating a semblance of civil administration across the country.

There still is a chance the killings could follow a different script, fracturing the shaky alliance between the U.S. and Afghan governments. The Taliban on Tuesday vowed to behead foreign troops “in every corner of the country,” and insurgents fired on an Afghan government delegation visiting the village where the shooting occurred.

But public protests and Taliban counterattacks so far have been less significant than many U.S. officials had expected, said several who described internal administration reaction on the condition of anonymity.

Troubled as the current U.S. military deployment is, American officials say a hasty drawdown could pose greater risks for Obama and Afghan President Hamid Karzai. Although he is furious over the killings, Karzai’s public expressions of anger also serve to insulate him from accusations by political rivals that he is too deferential to the Americans.

In previous crises — most notably, the Koran burnings — Karzai has sought to increase his leverage in negotiations with Washington over the contours of the American presence in Afghanistan once U.S. and NATO combat operations end in 2014. Karzai has said that he wants a smaller, more restricted U.S. presence right away, but he doesn’t favor a wholesale American departure, according to diplomats in Kabul, because U.S. troops, and U.S. financial assistance, are essential to propping up his government.

There are about 91,000 U.S. troops in Afghanistan. Obama has ordered the Pentagon to remove 23,000 of them by September, but he has not decided on the pace of further reductions despite calls on Capitol Hill and within his administration for a steeper troop drawdown.

Vice President Biden and some others in the White House argue that the large military presence has become corrosive and counterproductive. If Obama sides with them, he risks opposition from his top military commanders as well as campaign attacks from former Massachusetts governor Mitt Romney, should he become the Republican presidential nominee.

The top U.S. general in Afghanistan, Marine Gen. John R. Allen, has told senior administration officials that he would prefer there be no more reductions — beyond the 23,000 already planned — before the end of 2013. A senior U.S. official sympathetic to Allen said the military “footprint would be so diminished that we’d lack the connectivity to support the Afghan security forces nationwide” if there were additional drawdowns next year.

With less U.S. assistance to Afghan forces, military officials warn, insurgents could reclaim recently pacified areas in the south before the Afghans are capable of protecting those places themselves.

Although polls show that a narrow majority of Americans no longer think the Afghan war is worth fighting, U.S. officials say another round of troop reductions also could scuttle efforts to forge a peace deal with the Taliban while accelerating the rearming of ethnic militias and prompting NATO allies to withdraw more of their forces.

“There will be an awful lot of gnashing of teeth over the coming days and weeks, but when all this shakes out, the overall approach won’t fundamentally change,” said one administration official who is skeptical of the current strategy. “The costs of doing so are too great.”

That often is the conclusion in Washington and Kabul after incidents that initially appear insurmountable. When the Afghan government sought to ban all private security guards in late 2010 — a decision that could have forced many development contractors working for the U.S. Agency for International Development to cease operations — intense lobbying by U.S. officials led Karzai to revise his edict and delay its implementation.

Similar dynamics have played out after significant civilian casualties from errant bombings and nighttime raids. Karzai has vociferously complained and threatened to prevent the use of airstrikes and night operations, leading U.S. commanders to impose new restrictions on those tactics, but they have refused to accede to his insistence for a ban.

Seeking to assuage Afghan anger, Obama said Tuesday that he told Karzai: “The United States takes this as seriously as if it was our own citizens and our own children who were murdered.”

“The killing of innocent civilians is outrageous and it’s unacceptable,” he said. “It’s not who we are as a country, and it does not represent our military.” Obama pledged a thorough investigation by the Pentagon.

Some U.S. and Afghan officials caution that a series of events — the killings Sunday, the Koran burnings and the emergence in January of an Internet video showing three Marines urinating on the corpses of Taliban fighters — have inflamed so many Afghans that Karzai will be more insistent in demanding significant changes to U.S. operations.

The Obama administration may be more willing to compromise because it is keen to negotiate a long-term security partnership with Afghanistan — which would permit U.S. forces to remain for training and counterterrorism purposes — before a NATO summit this May.

Karzai already has won a concession, inked last week with Allen, to take control of U.S.-run prisons in six months, provided his government meets various conditions.

But in those talks, Karzai’s hand was strengthened by the large protests that erupted in several Afghan cities after the Korans were burned. Although U.S. officials were incensed that he did not do more to call for calm — the resulting violence claimed the lives of six U.S. troops and two dozen Afghans — the demonstrations were an expression of genuine Afghan revulsion at the desecration of the Muslim holy book. It did not matter that the decision to send the books to a burn pit at Bagram Airfield appears to have been an accident.

By contrast, what seems to Americans to be a far more despicable act — the killing of 16 civilians, most of them women and children — has led to fewer demonstrations in Afghanistan.

“Everyone here thought the protests would be much greater with 16 people slaughtered,” said a U.S. civilian adviser at the NATO headquarters in Kabul. “But only one act shocked the conscience here. The burning of the Korans was seen as an affront to Islam. To many Afghans, who have lived through 30 years of war, the killings are not as big of a deal.”

The inability to accurately predict how Afghans would react, the adviser said, “shows how little we know about this place after a decade of war.”