WASHINGTON — President Obama assumed full ownership of the war in Afghanistan last night with a speech arguing that the fastest way out of the conflict is a rapid and significant escalation of it. But the muted response from key Democratic congressional leaders and the skepticism about an exit strategy from Republicans signaled that the president faces a stiff fight to sell the policy.

Obama adopted the risky approach of both calling for a sizable troop surge — bigger in terms of percentage than the Iraq surge ordered by then-President George W. Bush — and outlining an exit strategy in the same speech. That was a clear acknowledgement of the fragile state of public opinion after eight years of conflict in Afghanistan, as well as the political divisions.

Obama stood his ground against his critics and wrapped his new policy in a call for the national unity that existed immediately after the attacks of Sept. 11, 2001. His speech was clearly argued and reflected his determination to chart his own course to disrupt al-Qaida while preventing Afghanistan from becoming a quagmire like Vietnam.

While he accepted most of the request for troops from his top commander in Afghanistan, the reshaping of the timing and deployment of those forces during the decision-making process allowed White House officials to argue that the result was the president's own, not a rubber-stamp of the Pentagon's vision.

PUBLIC OPINION

But those changes — and the commitment to begin leaving Afghanistan in July 2011 — may not be enough to head off a major battle within his own party to fund an expanded war.

The president's main audience was the American public. In the most recent Washington Post-ABC News poll, 52 percent of respondents said the war there was worth fighting, with Republicans agreeing by 2 to 1, Democrats disagreeing by more than 2 to 1 and independents split down the middle.

Obama's political standing depends on the military's ability to successfully implement the new strategy and on his own ability to maintain public confidence through what is likely to be a period of partisan debate and rising U.S. casualties. Democrats worry privately that the escalation, even with talk of an endgame, will demoralize their liberal base and dampen turnout in next year's elections.

Peter Feaver, a political scientist at Duke University who worked in the Bush White House analyzing public opinion on Iraq, said that as Obama begins his effort to sell the new strategy, he is in a far stronger position politically than Bush was when he announced the surge policy in January 2007. But he said mixed signals during the decision-making process forced Obama "to do a sharp pivot back" toward escalation, complicating his task of rallying public opinion.

William Galston of the Brookings Institution argued that Obama has in the past demonstrated the rhetorical and communication skills needed to gain the public's confidence, and said he expects that the president will be able to do so again.

But he added, "That doesn't mean he's going to get rich politically off this decision. This is not a poll-number-enhancing decision. But not everything that presidents are called upon to do in the national interest enhances poll numbers."

There are other audiences that the president and his national security and political teams must contend with in the coming months.

In the House, as many as half of Democrats may oppose the administration's request for money to support the surge, forcing Obama to rely on a big block of Republican votes to pass the legislation.

MESSAGE FOR KARZAI

Reactions last night illustrated the challenging environment for the president. Liberal Democrats expressed opposition to any escalation, while Democratic leaders signaled their reservations by saying they will take time to study the plan. Republicans applauded the troop increase but almost uniformly warned about sending mixed messages with talk of leaving.

But that exit strategy appeared aimed at another important audience: the government of Afghan President Hamid Karzai.

Obama's statement that, under his plan, U.S. forces could begin leaving Afghanistan in July 2011 was meant as much to warn the Karzai government that it cannot count on unlimited American support.

"The days of providing a blank check are over," he said.

Elsewhere in the world, Obama must convince adversaries that he will not waver in this fight while continuing to woo NATO allies to supply more troops of their own. Some have made commitments, but not yet enough. Obama said he is confident that more forces will be pledged "in the days and weeks ahead." But public opinion of the war in many of those countries is even more negative than it is in the United States.

Obama's address was quietly received by military cadets at West Point. But there were a few applause lines, including one that summed up the challenge before him.

"I refuse to accept the notion that we cannot summon that unity again," he said. "I believe with every fiber of my being that we — as Americans — can still come together behind a common purpose."