Osama bin Laden was why the United States went to war in Afghanistan. His death, coming at a moment when President Obama is considering the size and speed of his promised troop drawdown in the increasingly unpopular conflict, seems likely to change the calculation surrounding any exit strategy.

The question is: Will it accelerate or put the brakes on that withdrawal?

Obama had set this summer as the date when he would begin pulling U.S. forces out of Afghanistan. But with influential Pentagon voices resisting any dramatic move, expectations had been growing that the pullout would be more gradual than many of his fellow Democrats had hoped.

At the heart of the debate is the question of what the real goal is in Afghanistan: Rooting out al Qaeda, or the trickier, more ambitious aim of counterinsurgency, which requires a prolonged engagement aimed at bolstering and legitimizing its government.

Less than a day after Obama announced that bin Laden was dead, both sides of that debate contended that the al Qaeda leader’s removal bolstered their own approach.

Those who had been the champions of the president’s fall 2009 decision to send 30,000 additional troops to Afghanistan insisted that the removal of bin Laden should be seen as evidence the current strategy is working and an argument for continuing it.

“I think the killing of bin Laden gives us increased momentum for the war in Afghanistan,” said Sen. Joseph I. Lieberman (I-Conn.), chairman of the homeland security committee. “If I were [Taliban leader] Mullah Omar, I’d be frightened right now.”

But Senate Armed Services Committee Chairman Carl Levin (D-Mich.), who had opposed the troop surge, insisted he still believes Obama will begin a “robust reduction” in July.

“That instinct would be reinforced” by the bin Laden killing, Levin added.

At a minimum, the development seems likely to have given the president more credibility on the issue — and more political maneuvering room.

Polls have shown a combat-weary public souring not only on what the president had called “the war we have to win,” but also on the commander-in-chief’s leadership of it as it approaches the beginning of its second decade.

In the most recent Washington Post-ABC News survey, conducted late last month, 49 percent of respondents said they disapproved of Obama’s handling of the war, while only 45 percent approved. That was the most negative the public had been in the history of the poll, and it marked a sharp decline from January, when 49 percent had approved of the way that Obama was dealing with Afghanistan.

But underlying that number was a growing disillusionment with the mission itself. The previous month, the survey had shown that nearly two-thirds of Americans no longer believed that the war in Afghanistan was worth fighting.

The renewed debate over the mission also comes at a time when staggering budget deficits have put more pressure on defense spending. Meanwhile, the CIA has estimated that 100 or fewer al Qaeda operatives remain in Afghanistan.

Pollsters from both parties say it is not yet clear what message the public will take from bin Laden’s death: That it is time to turn the page from Afghanistan, or that persistence is what pays there. But it is not out of the question that the result might actually be something of a reversal of the political winds in each of the two parties.

Where Obama’s potential 2012 rivals have been critical of his plans to draw down the troops, “I would not be surprised to see Republicans candidates approaching this rather gingerly,” said GOP pollster Glen Bolger.

But at the same time, said Democratic pollster Peter Hart, “my sense is that the president could receive some support on the issue of resolve — resolve to be able to follow through and finish the job.”