In a move Democrats criticised as gamesmanship, Senate Republicans on Thursday brought up the withdrawal measure and quickly dispatched it on a 93-6 vote.
The proposal would have allowed "only forces that are critical to completing the mission of standing up Iraqi security forces" to remain in Iraq in 2007.
In a daylong House debate, Republicans defended the Iraq war as a key part of the global fight against terrorism while Democrats assailed the US president's war policies and called for a new direction in the conflict.
Dennis Hastert, the Republican House speaker, said: "When our freedom is challenged, Americans do not run."
"This is a war that is a grotesque mistake", countered House Democratic leader Nancy Pelosi of California. She called for a fresh strategy – "one that will make us safer, strengthen our military, and restore our reputation in the world".
Republicans moved towards a vote on a resolution to reject any timetable for withdrawing US forces.
Congress roared into debate on the three-year conflict four months before midterm elections that will decide the control of both the House and Senate - and as George Bush was trying to rebuild waning public support for the conflict.
The administration was determined to get its message out: the Pentagon distributed a 74-page "debate prep book" filled with ready-made answers for criticism of the war.
"We cannot cut and run," the Pentagon battle plan says at one point, seemingly anticipating Democratic calls for a troop withdrawal on a fixed timetable.
As the debates got under way, the Senate sent the president an additional $66 billion for military operations in Iraq and Afghanistan and the same day.
The president has tried to rally support for the Iraq war in the days since the death of Abu Musab al-Zarqawi and the recent completion of a new Iraqi government.
But as the death toll and price tag of the conflict continue to rise, opinion polls show voters increasingly frustrated with the war and favoring Democrats to control Congress instead of the Republicans who now run the show.
Sensitive to those political realities, Republicans in both the Senate and House sought to put politicians of both parties on record on an issue certain to be central in this fall's congressional elections.