Sen. Arlen Specter (D-Penn.) opposes the troop buildup and is skeptical a drawdown could begin by July 2011, as the president indicated.
"I oppose sending 30,000 additional American troops to Afghanistan because I am not persuaded that it is indispensable in our fight against Al Qaeda," Specter said in a statement. "If Al Qaeda can operate out of Yemen or Somalia, why fight in Afghanistan where no one has succeeded?"
He added, "It is unrealistic to expect the United States to be out in 18 months, so there is really no exit strategy."
Specter's statement addressed a key point of contention with respect to the president's plan: a timeline for withdrawal. Mr. Obama indicated troops should begin to withdraw by 2011, but he did not say when they would be fully out of Afghanistan.
Senate Majority Leader Harry Reid (D-Nev.), for one, gave his unequivocal support for the president's plan. And he offered support for the timetable.
"President Obama made a convincing case that sending additional troops to Afghanistan to fight al Qaeda and other terrorist groups is critical to our national security," Reid said in a statement.
"More than anything, I am pleased that he made clear that our resources are not unlimited and our commitment is not open-ended," he continued. "By laying out a strategy that will begin to bring our mission to a close within the next 18 months, the president drew an essential distinction between his approach to the war and that of the previous administration."
Assistant Senate Majority Leader Dick Durbin (D-Ill.) said he is reserving judgment: "President Obama asked for time to make his decision on a new policy in Afghanistan. I am going to take some time to think through the proposal he presented tonight."
Sen. Barbara Boxer (D-Calif.) said she firmly opposes adding more troops: "I support the president's mission and exit strategy for Afghanistan, but I do not support adding more troops because there are now 200,000 American, NATO and Afghan forces fighting roughly 20,000 Taliban and less than 100 al Qaeda," she said.
Sen. Paul Kirk (D-Mass.), who filled the late Sen. Ted Kennedy's Senate seat, said he remains skeptical about a significant troop build up "when the legitimacy of our Afghan partner is in serious question."
Sen. Russ Feingold (D-Wisc.) stated flatly in a statement following the speech last night that he does "not support the president's decision to send additional troops to fight a war in Afghanistan that is no longer in our national security interest."
"It's an expensive gamble to undertake armed nation-building on behalf of a corrupt government of questionable legitimacy," he said. "Sending more troops could further destabilize Afghanistan and, more importantly, Pakistan, a nuclear-armed state where al Qaeda is headquartered."
On the House side, Speaker Nancy Pelosi (D-Calif.) released a statement Tuesday night that reserved judgment of the plan.
Meanwhile, Rep. Ike Skelton (D-Mo.), chair of House Armed Services Committee, said he is "pleased President Obama agreed to provide the resources to get Afghanistan right."
He added, however, "I have a number of questions to which I hope we can get answers—for example, the role of Pakistan, how specifically we will measure progress over time, what additional resources we will need on the civilian side of the effort, how we will manage strain on our forces, and how we expect the government of Afghanistan to be reformed."
Rep. Nita Lowey (D-NY), who chairs the foreign operations subpanel of the House Appropriations Committee, also gave reserved support for the president's plan.
"Sending our brave and patriotic service members into harm's way is a solemn responsibility, and President Obama has provided the thoughtful leadership it requires," she said. "However, in my judgment, the most critical questions that must be answered are the scope of our mission, benchmarks to measure progress, and plans for transferring security and governance responsibilities to the Afghans themselves."
Rep. Jim McDermott (D-Wash.) said the Bush administration made a "fatal mistake" when it turned its focus from Afghanistan to Iraq, but he added that he is unconvinced Mr. Obama's plan will work.
"The president's speech tonight did not convince me that his policy is worth supporting," he said. "Last week, I attended a memorial service for seven servicemen from the same striker brigade from Fort Lewis who were killed on the same day in Afghanistan. I will not vote to send another troop to Afghanistan until I'm convinced that this strategy will succeed."
Rep. David Obey (D – Wisc.), the Democratic chair of the House appropriations committee, told CBS News' Katie Couric last night that the war must be paid for. President Obama did not specify in the speech how he planned to cover the costs of the troop surge.
"The fact is we've been told all throughout the health care debate that we must pay for every dollar of that bill," Obey said. "Well if that's the case they why should we not also pay for this effort? This effort is not just going to cost $30 billion on top of what we're already spending in Afghanistan – it's going to cost over $90 billion in a year."
More on Afghanistan:
Full Text of Obama's Remarks
Bob Schieffer: "Defining Moment" of Obama Presidency
McChrystal "Absolutely" Supports Timeline
Troops, Families Brace for Surge
Congress Scrutinizes New Afghan Plan
Marc Ambinder's Analysis: Obama Taking Big Risk
Mark Knoller: No Mention of "Victory"
McCain: No Deadlines for Afghan Withdrawal
Rep. Obey: Afghan War Must Be Paid For
Obama's Surge Comes with Expiration Date
Who Offers the Better Deal in Afghanistan?
Liberals Chastise Afghanistan Troop Increase
Polling Analysis: Afghanistan 2009 Vs. Iraq 2007
CBSNews.com Special Report: Afghanistan