Washington ? When he addresses the nation next week on his Afghanistan strategy, President Obama will face the central challenge of explaining why he is escalating an eight-year-old war that is increasingly unpopular with the American public, while outlining plans for leaving it.

Obama’s prime-time remarks, tentatively scheduled for Tuesday, will begin the White House effort to sell his revised war plan — which under one leading scenario calls for sending 30,000 additional U.S. troops — to powerful skeptics within his party, reluctant allies abroad and an Afghan public uncertain whether international forces or the Taliban will win the war.

Administration officials say the speech will outline a modest endgame for Afghanistan that would allow U.S. forces to leave and set a general time frame for achieving that result. The remarks will last about 40 minutes, officials said, roughly twice as long as then-President George W. Bush took to outline his Iraq “surge” strategy nearly three years ago.

Obama’s speech is expected to include an appeal to NATO allies, which the president alluded to Tuesday, saying that “one of the things I’m going to be discussing is the obligations of our international partners in this process.”

“I’ve also indicated that after eight years — some of those years in which we did not have, I think, either the resources or the strategy to get the job done — it is my intention to finish the job,” Obama said during a news conference with visiting Indian Prime Minister Manmohan Singh. “And I feel very confident that when the American people hear a clear rationale for what we’re doing there and how we intend to achieve our goals that they will be supportive.”

What is emerging from White House discussions is a plan favored by Defense Secretary Robert Gates that would deploy between 30,000 and 35,000 additional U.S. troops and call on NATO allies to contribute another 10,000 soldiers. That would bring the total number of new allied troops to about 40,000, the number sought by Gen. Stanley McChrystal, the commander of U.S. and NATO forces in Afghanistan.

Gates is asking for help at a time when the European public, even more than Americans, opposes any military escalation in Afghanistan, and Obama has in the past told Gates that he doubts that NATO leaders will agree to send additional forces, according to White House officials.

There are currently 68,000 U.S. troops in Afghanistan.