The 218-208 vote Wednesday came as the top U.S. commander in Iraq told lawmakers the country remained gripped by violence but was showing some signs of improvement.
Passage puts the bill on track to clear Congress by week's end and arrive on the president's desk in coming days as the first binding congressional challenge to Bush's handling of the conflict now in its fifth year.
"Our troops are mired in a civil war with no clear enemy and no clear strategy for success," said House Majority Leader Steny Hoyer, a Democrat.
House Speaker Nancy Pelosi — the Democrat most credited with leading Congress into this head-to-head confrontation with President Bush — laid low on Wednesday, reports CBS News correspondent Sharyl Attkisson. She skipped the meeting with Gen. David Petraeus, opting for a phone briefing instead.
Republicans promised to stand squarely behind the president in rejecting what they called a "surrender date" handed to the enemy.
"Al Qaeda will view this as the day the House of Representatives threw in the towel," said Rep. Jerry Lewis, a Republican who is on the House Appropriations Committee.
The $124.2 billion bill would fund the war, among other things, but demand troop withdrawals begin on Oct. 1 or sooner if the Iraqi government does not meet certain standards. The bill sets a nonbinding goal of completing the troop pull out by April 1, 2008, allowing for forces conducting certain noncombat missions, such as attacking terrorist networks or training Iraqi forces, to remain.
House and Senate appropriators agreed to the legislation earlier this week. The Senate was expected to clear the measure Thursday, sending it to the president.
While Bush was confident the bill would ultimately fail because Democrats lacked the two-thirds majority needed to override a veto, he kept up pressure on lawmakers.
On the same day as the House vote, the president dispatched his Iraq commander, Petraeus, and other senior defense officials to Congress to make his case: Additional forces recently sent to Iraq are yielding mixed results and the strategy needs more time to work.
Petraeus told reporters sectarian killings in Baghdad were only a third of what they were in January, before Bush began sending in additional U.S. forces. He added that progress in the troubled western Anbar province was "breathtaking," and that he thought Iraqi Prime Minister Nouri al-Maliki was "doing his best" at leading the country.
But "the ability of al Qaeda to conduct horrific, sensational attacks obviously has represented a setback and is an area in which we're focusing considerable attention," Petraeus said.
Petraeus said he would not touch on the "minefield of discussions about various legislative proposals," but he noted that the new strategy in Iraq was just beginning. He said he planned to provide more details in early September.
Petraeus briefed his findings to lawmakers in a private room, where protesters outside chanted "Troops home now!" Republicans and Democrats alike emerged to say Petraeus had only confirmed their positions.
"This briefing reinforced our view that the solution in Iraq is a political solution," Hoyer told reporters. Also confirmed, he said, was "our belief that we must hold the Iraqis accountable for achieving real progress."
Rep. John Boehner, the House Republican leader, said Petraeus acknowledged there were challenges. "But considering where we are, I think the general feels good about the progress thus far," Boehner said.
Bush said he stands firm on his latest strategy for winning the war and dismisses as counterproductive the Democratic call for withdrawal.
"That means our commanders in the middle of a combat zone would have to take fighting directions from legislators 6,000 miles away on Capitol Hill," Bush said this week. "The result would be a marked advantage for our enemies and a greater danger for our troops."
Petraeus' comments Wednesday put a finer point on when the much-awaited decision about the length of the U.S. troop buildup may come, saying he will make an assessment of the conditions in Iraq in early September, and report back to Defense Secretary Robert Gates and other military leaders.
Gates has said he expects the assessment this summer, but this is the first time military leaders said it would not be until September.