"We better be damn sure we know what we're doing, all of us, before we put 22,000 more Americans into that grinder," said Chuck Hagel, the sole Republican to join 11 Democrats in support of the measure.
Joseph Biden, the panel's chairman, said the legislation is "not an attempt to embarrass the president ... It's an attempt to save the president from making a significant mistake with regard to our policy in Iraq".
Dick Cheney, the US vice-president, dismissed the congressional objections. During an interview with CNN he said "it won't stop us".
He said: "It would be, I think, detrimental from the standpoint of the troops.
"The congress has control over the purse strings. They have the right, obviously, if they want, to cut off funding. But in terms of this effort, the president has made his decision.
|"We better be damn sure we know what we're doing, all of us, before we put 22,000 more Americans into that grinder"|
Chuck Hagel, Republican senator
"We are moving forward. We are moving forward. We'll continue to consult with the congress. But the fact of the matter is, we need to get the job done."
Asked whether the White House bore responsibility for the bloody chaos in Iraq, Cheney defended the invasion in March 2003 to depose Saddam Hussein.
He said: "Saddam Hussein would still be in power. He would, at this point, be engaged in a nuclear arms race with [Iranian president Mahmoud] Ahmadinejad, his blood enemy next door in Iran.
"What we did in Iraq in taking down Saddam Hussein was exactly the right thing to do; the world is much safer today because of it."
Meanwhile John Kerry, the defeated presidential candidate in 2004, announced that he would not be seeking the Democratic nomination in 2008 and would concentrate instead on senate efforts to end the Iraq war.
He said in a speech on the senate floor: "I've concluded this isn't the time for me to mount a presidential campaign.
"It is the time to put my energy to work as part of the majority in the senate to do all I can to end this war.
"Bush's strategy has failed totally in Iraq"
Dimos, Hania-Crete, Greece
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"What happens here in the next two years may irrevocably shape or terribly distort the administration of whichever candidate is elected president."
Kerry would have faced a tough task overcoming the criticism of some Democrats who argue that he ran a lacklustre 2004 campaign that failed to take advantage of public doubts about Bush's leadership.
He also would have been up against a crowded and high-profile field of at least eight Democrats led by Hillary Rodham Clinton of New York and Barack Obama of Illinois.