Al Jazeera correspondent Viviana Hurtado said: "This is the first time in six years that Bush has had any questioning of his authority by the US congress.
"The chances of success [in Iraq] are essentially zero because the Iraqi people have no voice"
Non Sequitur, Cadiz, Spain
Send us your views"President Bush appears weaker in the eyes of Americans and in the eyes of the world."
Democrats have said that while they are unlikely to get the two-thirds vote needed to override a presidential veto the vote signifies congress' desire for a new direction in Iraq.
"The American people want our troops out, out, out of Iraq," said Robert Byrd, a Democrat senator, on the senate floor after the vote.
'Change of strategy'
Speaking on Wednesday, Nancy Pelosi, the Democrat and house speaker, appealed to Bush to respect the growing call for a change of strategy in Iraq.
"There is a new congress in town. We respect your constitutional role. We want you to respect ours," she said.
Senate Republicans could have blocked Tuesday's vote by using a 'filibuster', a parliamentary stalling tactic, but Mitch McConnell, a minority leader, said he decided it was better to allow Bush to veto the bill.
|Pelosi wants Bush to respect the growing call|
for a change of US strategy in Iraq [EPA]
McConnell questioned the validity of the March 31, 2008, deadline.
He said: "The date isn't tied to circumstances on the ground. It's completely arbitrary. They pulled it out of thin air.
"And the terrorists have already marked it on their calendar."
Bush has consistently rejected any time restrictions on the presence of US troops in Iraq, particularly after his recent commitment to deploy 30,000 more troops in the country.
Senate approval of the bill means both chambers of congress have formally called on the president to end US involvement in the war in Iraq during the course of the next year.
The House of Representatives passed legislation last week setting a mandatory troop withdrawal deadline of September 1, 2008.
The two chambers will try to work out a compromise before sending the bill to Bush next month.