Only hours after Gen. David H. Petraeus, the commander in Iraq, told lawmakers he needed more time to gauge the effectiveness of a troop buildup there, the House voted 218 to 208 to pass a measure that sought the removal of most combat forces by next spring. Mr. Bush has said unequivocally and repeatedly that he will veto it.

“Last fall, the American people voted for a new direction in Iraq,” said Speaker Nancy Pelosi, Democrat of California. “They made it clear that our troops must be given all they need to do their jobs, but that our troops must be brought home responsibly, safely, and soon.”

Republicans accused Democrats of establishing a “date certain” for America’s defeat in Iraq and capitulating to terrorism.

“This bill is nothing short of a cut and run in the fight against Al Qaeda,” said Representative Harold Rogers, Republican of Kentucky.

On the final vote, 216 Democrats and 2 Republicans supported the bill; 195 Republicans and 13 Democrats opposed it.

The Senate is expected on Thursday to approve identical legislation, which provides more than $95 billion for combat operations in Iraq and Afghanistan through Sept. 30, with the money conditioned on the administration’s willingness to accept a timetable for withdrawal and new benchmarks to assess the progress of the Iraqi government. Democratic leaders plan to send the bill to the White House early next week — coinciding with the fourth anniversary of Mr. Bush’s May 1, 2003, speech aboard an aircraft carrier when he declared the end of major combat operations before a banner that said “Mission Accomplished.”

At the White House, Dana Perino, the deputy press secretary, released a statement minutes after the vote, calling the bill “disappointing legislation that insists on a surrender date, handcuffs our generals, and contains billions of dollars in spending unrelated to the war.”

With the outcome essentially preordained, advocacy groups on both sides of the issue were readying campaigns to try to shape public opinion as the showdown unfolds.

Groups aligned with the Democrats plan to capitalize on the connection between the veto and the “mission accomplished” anniversary. Americans United for Change has produced a television commercial that replays scenes of Mr. Bush on the carrier and says: “He was wrong then. And he’s wrong now. It’s the will of one nation versus the stubbornness of one man.”

Allies of the president are mobilizing as well. The conservative Web site Townhall.com was organizing an online “no surrender” petition, and urging visitors to the site to tell the Democratic Party’s “rogues’ gallery that we will not stand for their defeatism,” adding, “While they may lack courage, our troops do not and they deserve the resources needed to win this war.”

With the vote barely behind them, House Democrats were already considering how to respond legislatively to Mr. Bush’s veto. Though there are differing ideas, Representative John P. Murtha of Pennsylvania, a Democrat who oversees defense appropriations, said his preference would be to “robustly fund the troops for two months,” and include benchmarks but no timetable for withdrawal.

The briefing by General Petraeus and other senior Pentagon officials appeared to do little to influence the House vote. Lawmakers said the commander had made no overt plea for them to oppose the legislation, which provides more money for the Pentagon than the president had sought for the war.

“I’m not going to get into the minefield of discussions about various legislative proposals,” General Petraeus told reporters at the end of the two briefings. “I don’t think that is something military commanders should get into.” The general pointed to a drop in sectarian killings and security gains in Anbar Province as improvements in recent weeks but referred to reversals as well. “The ability of Al Qaeda to conduct horrific, sensational attacks obviously has represented a setback and is an area in which we are focusing considerable attention,” he said.

Lawmakers, speaking on condition of anonymity because the briefings in the House and Senate were classified, said that while the general had pointed to successful weapons seizures and a substantial drop in killings as evidence of progress, he and the others could not quantify how they would evaluate future success.

Lawmakers who attended a session said General Petraeus had said he would need until September to judge whether the troop increase was meeting its goals.

In addition to General Petraeus, lawmakers in the House and Senate heard from Deputy Secretary of Defense Gordon England, Deputy Secretary of State John D. Negroponte and Adm. Edmund P. Giambastiani Jr., vice chairman of the Joint Chiefs of Staff. As they walked into the House briefing, the officials were greeted by about a dozen war protesters, some of whom shouted: “War criminal! War criminal!” One woman walked alongside the general, urging him in a softer tone to consider her point of view.

After the briefing, Representative Steny H. Hoyer of Maryland, the majority leader, disputed criticisms that Democrats were trying to end the war before giving the administration’s plan a chance to succeed. “Nobody is saying get out tomorrow,” Mr. Hoyer said, noting that the legislation would allow American troops to stay in Iraq to battle terrorist groups.

He and Representative John A. Boehner of Ohio, the Republican leader, differed on what emerged from the briefing as the most significant cause of violence in Iraq. Mr. Hoyer attributed it to sectarian strife, while Mr. Boehner cited Al Qaeda in Mesopotamia.

Republicans took issue with the absence from the briefing of Ms. Pelosi, who had talked by telephone to General Petraeus. “This latest insult to our troops should come as no surprise since others in the Democrat leadership have declared the war lost,” said Representative Geoff Davis, Republican of Kentucky. A similar message reverberated on talk radio to cable television news programs on Wednesday.

Aides said Ms. Pelosi was working on the vote count in her office and meant no disrespect to the military commander but had already heard his Iraq report. Democrats also noted that Senator John McCain, Republican of Arizona and a defender of the war, was out of town, announcing his presidential campaign in New Hampshire.

Democrats sought to portray their approach as reasonable and called for Mr. Bush to reconsider before sending the bill back to Congress, where Republicans hold sufficient votes to sustain his position.

“I believe that this legislation, if people were to just take their time and read it, is the exit strategy that the president ought to be pleased to receive,” said Representative James E. Clyburn of South Carolina, the Democratic whip.

But Republicans called it a dubious attempt at micromanaging the war and said Democrats were also seizing the opportunity to stuff the bill with home-state spending.

The president’s allies, aware of public dissatisfaction with the war, acknowledged the difficulties on the ground in Iraq while portraying the Democratic approach as a prescription for defeat.

“It’s been ugly, it’s been difficult, it has been very painful,” said Representative David Dreier, Republican of California. “We all feel the toll that has been taken and are fully aware of the price we are paying, especially in a human sense. But we do not honor those who have sacrificed by abandoning the mission.”