On his recent Asian trip, President Obama backed away from his 2011 deadline to begin withdrawing troops from Afghanistan. Why the change of heart when polls show declining popular support for the war? Perhaps because, unlike most of the American public, the president is paying attention to our enemies.

For example, most Americans haven’t heard of Ahmed Sidiqi. Barack Obama has.

NATO troops arrested Sidiqi, a 36-year-old Afghan-German, in July in Kabul. Under questioning, he admitted meeting with Younis al-Mauretani, a senior al-Qaeda leader in the tribal areas of Pakistan. The purpose of that meeting: to be briefed on al-Qaeda’s plan to make the streets of Europe run red.

Mauretani’s plan called for multiple “Mumbai-style” attacks launched simultaneously in several European countries. In 2008, you’ll recall, terrorists launched a vicious ground assault in Mumbai, roaming the Indian city and slaughtering innocents. A shadowy handler back in Pakistan directed the gunmen’s attacks via cell phone.

Without NATO boots on the ground, the plot against Europe might never have been uncovered. Without America’s military presence, the subsequent predator-drone strikes that wiped out more than a half-dozen al-Qaeda assets involved in the plot would have been impossible.

The wilds of Afghanistan and Pakistan are al-Qaeda central. To quit the area before we’ve rooted out the terrorists would hand al-Qaeda a propaganda victory of immeasurable value.

Worse, it would cede them a sanctuary from which they could mount fresh strikes at the West with virtual immunity. To cut and run from Afghanistan before we’ve finished the job is to pave the way to the next 9/11.

Finishing al-Qaeda requires two essential and related actions.

One is establishing an Afghanistan that governs and defends itself. This mission is not nation-building, but the vital task that must be done to take space away from the Taliban to operate. It is the precursor to defeating the Taliban and forcing what is left to disarm and reintegrate peacefully into the Pashtun communities that span the borders of Afghanistan and Pakistan.

Defeating the Taliban is a prerequisite for destroying al-Qaeda. The two organizations protect and support each other.

The second task is defeating the Taliban within Pakistan and destroying al-Qaeda.

This work must mostly be done by Pakistan -- a task they will never undertake if they believe the United States lacks the resolve to stick it out until the job is done.

Al-Qaeda knows it can lose this war. It is for this reason that they have been trying to build up an alternative base of operations in Yemen -- and why they are desperately seeking any means to strike at the West from “terrorism tourists” aimed at the capitals of Europe to the underwear bomber, the aborted Times Square attack, and the mail bombs recently sent to the United States.

The good news is that from al-Qaeda’s perspective these have all been a grave disappointment -- ineptly organized or thwarted by good intelligence, law enforcement and military operations.

Al-Qaeda knows it can lose. Americans should know we can win. Walking away from an arbitrary deadline for troop withdrawal is a first step in reassuring the public and our allies that we’re “in it to win it.” Many reluctant to back a grinding, half-hearted struggle will back a full-throated commitment to victory.

Last month, a Harris Poll of more than 3,000 adult Americans found just a quarter wanted the United States to withdraw its troops now; only a third supported any timeline for withdrawal.

The American public does not want to lose the war in Afghanistan.

They want an effort that is smart and tough enough to finish the job successfully. Completing that mission is essential to keeping our homeland safe.

James Jay Carafano, director of the Allison Center for Foreign Policy Studies at The Heritage Foundation.