The death of Osama bin Laden and growing pressure from Congress to shrink the U.S. footprint and expense in Afghanistan have given new impetus to those within the Obama administration who favor a swift reduction of U.S. forces, according to senior administration officials and leading lawmakers.

These members of the administration initially pressed for an approach that emphasized the targeted killing of insurgent leaders, rather than the broader, troop-heavy counterinsurgency strategy that President Obama ultimately embraced. They intend to argue in upcoming debates that the al-Qaeda leader’s demise is proof that counterterrorism is a more reliable and cost-effective tactic for the next phase of the nearly decade-old war.

Even before the death of bin Laden, the confluence of the national debt crisis, the 2012 election, and events on the ground had bolstered arguments that the administration’s plans to remake Afghanistan’s government and economy went too far beyond the goal of safeguarding U.S. security.

Current expenditures of $10 billion a month are “fundamentally unsustainable” and the administration urgently needs to clarify both its mission and exit plan, Sen. John F. Kerry (D-Mass.) said Tuesday.

A senior administration official involved in Afghanistan policy insisted that “there will be no re-litigation” of the strategy that has brought 30,000 more U.S. troops and hundreds of additional U.S. diplomats to the war zone since early last year. “We’re on a clear path set by the president,” the official said.

But the official said the killing of bin Laden “may have a significant effect going forward on the setting of milestones and the pace and slope” of the U.S. troop withdrawal scheduled to take place between July and the end of 2014.

Administration officials, who spoke on the condition of anonymity to describe internal thinking, emphasized that Obama and his national security team have not begun discussions on the withdrawal nor has the military made a recommendation.

At a Tuesday hearing of the Senate Foreign Relations Committee he chairs, Kerry said he did not advocate a “unilateral, precipitous withdrawal” of U.S. forces. But, he said, “I do think that we ought to be working towards achieving the smallest footprint possible.”

Kerry is a longtime friend and former Senate colleague of Vice President Biden, who led the administration faction arguing that counterterrorism was a more reliable and cost-effective tactic against al-Qaeda. The senator from Massachusetts is often a leading indicator of administration thinking. Secretary of State Hillary Rodham Clinton and Defense Secretary Robert M. Gates — whose departments and personnel have carried out the counterinsurgency strategy — advised in favor of Obama’s ultimate decision.

“One threshold really needs to be both stated and restated as we consider the options,” Kerry said. “And that is that it is fundamentally unsustainable to continue spending $10 billion a month on a massive military operation with no end in sight.”

Kerry has played an active role in supporting the administration’s strategy and in helping keep Hamid Karzai, the often troublesome Afghanistan president, in line. But he questioned the administration’s “lack of clarity” on reconciliation talks with the Taliban and the outline of a political solution that top administration policymakers have said are among the top U.S. priorities this year.

“Looming large in front of us is the pregnant question: What is the political solution? We need to make our ultimate goals absolutely clear for the sake of the American people, Afghans, Pakistanis and everyone else who has a stake in the outcome,” Kerry said.

The senior administration official said that it was not clear whether bin Laden’s death would cause the Taliban to separate from al-Qaeda. “But his death makes that more likely, which could give traction to reconciliation efforts between the Taliban and the Afghan government.”

Lawmakers of both parties have expressed increasing impatience. “The question before us is whether Afghanistan is important enough to justify the lives and massive resources that are being spent there, especially given our nation’s debt crisis,” Sen. Richard G. Lugar (Ind.), the senior Republican on the Foreign Relations Committee said at the hearing.

“The president should not just withdraw an arbitrary number of troops,” Lugar said. “Rather, he should put forward a new plan that includes a definition of success in Afghanistan based on the United States’ vital interests and a sober analysis of what is possible to achieve,” he said.

In the 10 days since bin Laden’s death, many legislators have called for the United States to speed its withdrawal from Afghanistan, beginning with Obama’s planned drawdown of an unspecified number of troops this summer.

The U.S.-led coalition, with a current total of about 140,000 troops, two-thirds of them American, has pledged a complete combat withdrawal by 2014.

There is little dispute in the White House and among lawmakers that this year has brought substantial military gains against the Taliban. But assessments of the other elements of the strategy — such as improving the economy and the government in ways that can sustain hard-won security — are less positive.

Many have questioned the feasibility of plans to recruit and train as many as 400,000 Afghan security forces to take over once foreign troops depart.“Despite our best efforts, there are challenges — corruption, predatory behavior, incompetence — still evident within the Afghan army and police,” Kerry said. “On top of these problems, there is the question, ultimately, of money, resources.”

While the annual cost of maintaining the Afghan forces is estimated at up to $10 billion, Afghan tax revenue totals about $2 billion. “So who will pay the bills to avoid having those armed soldiers and police mobilized as part of the next insurgency?” Kerry asked.

As Obama awaits a July withdrawal recommendation from Gen. David H. Petraeus, commander of the U.S.-led coalition in Afghanistan, “our understanding is that the President’s intention is not for it to be a pittance,” a U.S. military official said.

“I’m not at all surprised that people on the Hill and elsewhere in the federal government want to use this to have a broader debate about where we’re spending their money,” the official said. But “I don’t think there’s a lot of deep questioning right now among the [military] inner circle on how do we now turn” bin Laden’s death into a new strategy.

“The military’s perspective going into this decision making process is not about renewing the debate over the strategy,” the official said. “We’ve been given our mission. It’s a strategy we believe is working and that we know has a deadline.”

U.S. military officials in Afghanistan have pushed to stay as aggressive as possible against the Taliban and have urged a smaller troop drawdown in the short term.

“What has been the U.S. administration’s primary argument for being in Afghanistan — the al-Qaeda threat — has now been diminished,” said one Western diplomat in Kabul. “It will only strengthen the argument that you can now begin the military withdrawal.”

Correspondent Joshua Partlow in Kabul contributed to this report.