Democrats complained about Obama's escalation of the 8-year-old war, however. And Republicans are unhappy with his promise to withdraw troops in 18 months. But Congress appears nevertheless willing to approve the buildup's $30 billion price tag.
Sen. John McCain, who lost to Obama in last year's presidential election, reiterated Wednesday that while he supports the president's build up, he believes it's a mistake to signal in advance when a troop withdrawal might begin. Obama said in his prime-time West Point speech Tuesday that it could commence as early as July 2011.
The Arizona Republican said: "We don't want to sound an uncertain trumpet to our friends in the region."
On Capitol Hill, Congress is ready to use two days of high-profile hearings on the war, beginning later Wednesday, to express its misgivings. Obama's escalation strategy won quick backing from NATO allies. Afghan leaders praised the speech, but had questions about the 18-month timetable for withdrawal.
And a Taliban spokesman said Wednesday that Obama's plan was "no solution" to Afghanistan's troubles.
Of Karzai, Biden said the plan was an unmistakable warning. "The purpose is to make it clear to Karzai and his government, which have up to now been unwilling to step up to the ball, to make it clear that you now have to step up to the ball," the vice president said.
Obama pledged Tuesday night to an audience of Army cadets at the U.S. Military Academy that the shift from surge to exit strategy would depend on the military situation in Afghanistan.
"We will execute this transition responsibly, taking into account conditions on the ground," Obama said, declaring that the nation's security was at stake and that the additional troops were needed to "bring this war to a successful conclusion."
Sen. Carl Levin, chairman of the Senate Armed Services Committee, which planned to grill top administration officials Wednesday on Obama's decision, said that he expected the administration to submit a new war spending request and that Democrats would back it.
The planned infusion of 30,000 U.S. troops would raise the total American military presence in Afghanistan to about 100,000. Defense Secretary Robert Gates was expected to tell Levin's panel that the president's strategy "will make real and measurable progress over the next 18-24 months," said spokesman Geoff Morrell.
Biden was asked about doubts he was said to have had about escalating the war.
"I've never publicly said what my position is because I reserve that for the president," he replied. "But I was skeptical of taking our eye off the ball. The ball is al-Qaida. That's the reason we're there. They are in Pakistan, the Taliban leadership is in Pakistan. And I wanted to make sure the focus stayed on those two elements of our concern and didn't sort of morph into a nation-building exercise that would tie us down for 10 years and in fact not be of any assistance in meeting what is the real threat to the U.S. -- that is al-Qaida and the most extreme forces that are in Pakistan and wanting to topple Pakistan."
Many Democrats said they weren't convinced that sending more troops would hasten an end to the war. They also question whether the money used for troop deployments will drain resources from other domestic priorities, like health care and job creation.
Sen. Russ Feingold, D-Wis., called the plan "an expensive gamble to undertake armed nation-building on behalf of a corrupt government of questionable legitimacy."
After meeting Wednesday with Karzai, U.S. Gen. Stanley McChrystal called Karzai's reaction to the new U.S. strategy "really positive. The president was very upbeat, very resolute this morning."
McChrystal, Obama's field commander in Afghanistan, said U.S. and NATO forces would hand over responsibility for the fight against the Taliban to Afghan security forces "as rapidly as conditions allow."
Afghan Interior Minister Hanif Atmar, who also met with McChrystal, sought more details about how the Afghan security forces would be trained and expanded in the next 18 months -- a time frame that he said was too short for a complete handoff from international forces.
"That kind of time frame will give us momentum," Atmar said. "We are hoping that there will be clarity in terms of long-term growth needs of the Afghan national security forces and what can be achieved in 18 months."
NATO Secretary-General Anders Fogh Rasmussen said he expected the allies to bolster the American buildup with more than 5,000 additional troops. He said the best way to overcome widespread public opposition in Europe is by demonstrating progress, starting by transferring control of parts of the country to the Afghan government.
At a meeting of foreign ministers in Athens, Greece, U.S. Deputy Secretary of State James Steinberg said: "Some countries are ready now to make commitments to provide additional troops or additional funds, some are now just examining it. We understand that they need a little bit of time to digest exactly what the president's proposed."
French President Nicolas Sarkozy hailed Obama's speech as "courageous, determined and lucid" but stopped short of pledging additional French troops.