Washington ? The nation’s top military officer and its top diplomat made clear Thursday that President Barack Obama rejected the advice of his generals in choosing a quicker path to winding down the war in Afghanistan.

The Obama troop withdrawal plan, widely interpreted as marking the beginning of the end of the U.S. combat role in Afghanistan, drew criticism from both sides of the political aisle on Capitol Hill. Some Republicans decried it as undercutting the military mission at a critical stage of the war, while many Democrats called it too timid.

Sen. John McCain, R-Ariz., took a swipe at Obama from the Senate floor, questioning the timing of his troop pullout plan.

“Just when they are one year away from turning over a battered and broken enemy in both southern and eastern Afghanistan to our Afghan partners — the president has now decided to deny them the forces that our commanders believe they need to accomplish their objective,” McCain said.

Obama announced Wednesday night that he will pull 10,000 troops from Afghanistan by December and another 23,000 by the end of next summer.

On Thursday, the president spoke at New York’s Fort Drum to troops and commanders of the Army’s 10th Mountain Division. Its headquarters staff is in southern Afghanistan and its soldiers have been among the most frequently deployed in Iraq and Afghanistan over the past decade.

Obama, perhaps responding to the flank of criticism from the right, said that he is not pulling home troops “precipitously” or risking the gain they’ve achieved.

“We’re going to do it in a steady way to make sure that the gains that all of you helped to bring about are going to be sustained,” he said. “Because of you, we’re now taking the fight to the Taliban, instead of the Taliban bringing the fight to us. And because of you, there are signs that the Taliban may be interested in figuring out a political settlement, which ultimately is going to be critical for consolidating that country.”

Navy Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, told the House Armed Services Committee that he supports the Obama plan, although he had recommended a less aggressive drawdown schedule.

Obama’s approach adds risk to the military mission, Mullen said. But he added, “It’s manageable risk.”

Army Gen. David Petraeus, the top U.S. commander in Afghanistan, said later that he, too, had recommended a more gradual withdrawal — as had Marine Gen. James Mattis, who as commander of U.S. Central Command is Petraeus’ immediate boss and overseer of all U.S. military operations in the greater Mideast.

Petraeus, appearing before the Senate Intelligence Committee, which is considering his nomination to become CIA director, had a telling exchange with Sen. Carl Levin, D-Mich. Levin asked the general whether he would resign if he felt he could not support Obama’s decision.

“I’m not a quitter,” Petraeus replied. “This is something I have thought a bit about. I don’t think it’s the place for a commander to actually consider that kind of step unless you are in a very, very dire situation.”

In the same exchange, Petraeus appeared to suggest that he had vigorously opposed the timeline that the president chose. Levin asked Petraeus whether he felt comfortable supporting the plan now.

Petraeus wouldn’t sign up for that without qualification. He implied he remains uneasy about the decision but said he does not think the plan is destined to fail.

Petraeus said he was returning to Kabul today to work with his staff on how to implement the Obama plan.

Obama’s plan will leave 68,000 U.S. troops in Afghanistan after the drawdown. Most of those troops would gradually come home over the next two years, and the U.S. plans to close out its combat role in Afghanistan by 2015.