Dana Perino, the White House press secretary, said Bush would veto the measure and that a "clean" emergency funding bill, without withdrawl dates, should be put forward.
Perino said the Democrats were taking the war debate "down a well-worn path that calls for arbitrary withdrawal from the battlefield, despite the gains our military has made over the past year.
"Iraq is still under foreign occupation and Iraqis continue to die in great numbers"
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"These votes, like the dozens of previous failed votes, put the interests of radical interest groups ahead of the needs of our military and their mission," she said.
Steny Hoyer, the senate democratic majority leader, said: "All of us here want to succeed in Iraq. All of us here want to make our nation and the American people safer.
"But after more than four and one half years of pursuing the president's failing stay-the-course strategy, we are not achieving either objective." Liberal and anti-war Democratic members of the house unexpectedly backed the bill assisting its success.
Strongest bill yet
Lynn Woolsey, Barbara Lee and Maxine Water, three anti-war legislators, said: "While this bill is not perfect, it is the strongest Iraq bill to date.
"This is a concrete step in the right direction, and an important marker for this congress to lay down."
Bush would be required to transfer combat operations to supporting Iraqi security forces under the bill.
The use of torture would be banned under the measure and the remainder of Bush's $196bn request for the wars in Iraq and Afghanistan would be deferred.
The funding would be expected to last four months.