Most Republicans backed the president's decision to send more troops.
They claimed, however, he was playing politics by setting an "arbitrary" withdrawal deadline while insisting that any transfer of responsibility to the Afghan government will ultimately be based on conditions in that country.
They also argued he had inadvertently strengthened the hand of Taliban and al Qaeda extremists by allowing them to know when a U.S. departure from the war-torn country would begin.
Several members of the Democratic caucus, on the other hand, expressed unease with the president's decision to send thousands of additional troops over the next several months. They questioned whether the war is winnable.
Obama's blueprint was closely examined during appearances before two key committees by Secretary of State Hillary Clinton, Secretary of Defense Robert Gates and Adm. Mike Mullen, the chairman of the Joint Chiefs of Staff.
"I disagree with the president's decision to personally relay to our enemies when they can regroup and when they can retake Afghan territory," said Florida GOP Rep. Connie Mack, a member of the House Foreign Affairs Committee.
"I simply cannot understand and cannot agree with this approach." Obama's decision "emboldens our enemies (and) allows them to prepare and plan."
Announcing a firm date for starting an American withdrawal while also saying such a withdrawal depends on conditions in Afghanistan "are two incompatible statements," said Sen. John McCain of Arizona , the Senate Armed Services Committee's ranking Republican.
"You either have a winning strategy ... and then once it's succeeded then we withdraw or, as the president said, we will have a date (for) beginning withdrawal in July 2011," he said. "Which is it? It's got to be one or the other. It's got to be the appropriate conditions or it's got to be an arbitrary date. You can't have both."
Gates noted that the administration will conduct "a thorough review" of the Afghan strategy in December of 2010.
"If it appears that the strategy's not working, and that we are not going to be able to transition in 2011, then we will take a hard look at the strategy itself," he said.
"The president always has the freedom to adjust his decisions," Gates added. But he has made "a clear statement of his strong intent."
Obama's new deployment, estimated to cost $30 billion a year, will bring the total number of U.S. service members in Afghanistan to roughly 100,000.
NATO allies are expected to add at least another 5,000 troops to the more than 40,000 they have already contributed to the U.S.-led mission.
The new strategy is designed to eliminate al Qaeda in Afghanistan and help the Afghan government defeat the Taliban insurgency, while bolstering neighboring Pakistan's anti-terrorism efforts.
"The success of this operation depends on will and resolve," argued GOP Sen. Lindsey Graham of South Carolina. "I just don't want the July 2011 statement to be seen by our enemy (to mean) that we have somehow locked ourselves into leaving."
Clinton replied that she does "not believe we have locked ourselves into leaving, but what we have done ... is to signal very clearly to all audiences that the United States is not interested in occupying Afghanistan."
The Afghan people, Mullen noted, ultimately have to win the war by themselves. The U.S. military buildup is "about partnering and mentoring just as much if not more than it is about fighting."
The administration is not "going to throw these guys into the swimming pool and then walk away," Gates said in reference to Afghan military and civilian authorities. But it's important to establish a timeline in part to "build a fire under them, frankly, to get them to do the kind of recruitment, retention, training and so on for their forces that allow us to make this transition."
Gates and Mullen noted that the Afghan military is slated to increase from 134,000 troops in December 2010 to 170,000 by July 2011.
They also indicated that the initial transfers of responsibility will take place in areas marked by less fighting.
The administration's "timeline is clear," Mullen argued. The flexibility "is in where we transition (and) where we turn over responsibility."
White House Press Secretary Robert Gibbs dismissed GOP claims that the Taliban and al Qaeda could simply wait out the surge and return after the start of a U.S. withdrawal in 2011.
"I consider (it) to be a highly illogical argument (that) these people are going to recede into the woods, they're going to give up their land, they're going to give up what they control," he said.
"If that's the case, great. That would be the best outcome, because American forces would then take that real estate. ... If (the extremists) want to come back in July 2011 and start this process over again, they'll meet a far larger Afghan national security force to take them on."
Some Democrats, however, questioned the necessity of continuing the conflict.
"I'm really struggling with this," said Rep. Gary Ackerman, D-New York. "I'm trying to think this thing through."
Ackerman said he understood the need to prevent an extremist takeover of neighboring Pakistan - a nuclear power - but asked if that required an extended war in Afghanistan.
"I think the best I come up with is that we have a shack that's on fire, but it's located next to the dynamite factory," he said. "Is it worth risking the lives of those who respond to the fire in a place that may or may not hold a lot of value in and of itself?"
"We've been there eight years now and we're still talking about turning it around," said Rep. Bill Delahunt, D-Massachusetts. "Is (another) 18 months going to be sufficient?"
Rep. Donald Payne, D-New Jersey, blamed a recent Taliban resurgence in Afghanistan on neglect by the Bush administration since the start of the Iraq conflict in 2003. As a result, he argued, Obama was left with no good choices in Afghanistan.
"I don't like the increase in troops. I don't think we can win a war in Afghanistan," he said. "We have to quickly transition into having the Afghans take care of themselves."
The top House Democrat on the committee that controls war spending told reporters he remains skeptical despite Obama's speech and will try to attach benchmarks to a war funding bill he expects Congress to consider next year.
"The president was very persuasive, but I'm looking for facts," said Rep. John Murtha, D-Pennsylvania, chairman of the House Defense Appropriations Subcommittee. Murtha questioned if the situation in Afghanistan is a threat to U.S. national security and said: "I'm looking for how we can live with this thing. We've got plenty of problems here in the United States."
Murtha and other leading House Democrats have proposed an income tax surcharge on most Americans to finance the war in Afghanistan, but he acknowledged the proposal is unlikely to pass.
U.S.-led troops first invaded Afghanistan in response to the al Qaeda terrorist network's September 11, 2001, attacks on New York and Washington. The invasion overthrew the ruling Taliban, which had allowed al Qaeda to operate from its territory, but most of the top al Qaeda and Taliban leadership escaped the onslaught.
Taliban fighters have since regrouped in the mountainous region along
Afghanistan's border with Pakistan, battling U.S. and Afghan government forces on one side and Pakistani troops on the other. Al Qaeda's top leaders, Osama bin Laden and Ayman al-Zawahiri, are believed to be hiding in the same region.
"A stable security situation in Afghanistan and Pakistan, one that is sustainable over the long term by their governments, is vital to our national security," Gates stressed.
"By the same token, the current status quo in Afghanistan - the slow but steady deterioration of the security situation and growing influence of the Taliban - is unacceptable."
–CNN's Deirdre Walsh and Alan Silverleib contributed to this report