The House is expected to begin debate on a $124.3 billion war spending bill Thursday, though Democratic leaders were still struggling to round up the 218 votes necessary for passage.

“It’s within two or three votes right now,” said John P. Murtha, D-Pa., chairman of the Defense Appropriations Subcommittee.

Democrats face a difficult task. Republicans are largely united against the measure (HR 1591) and President Bush has threatened a veto over troop withdrawal language he says would hamper the war effort, as well as the billions of dollars Democrats added for domestic spending.

Early Thursday, the House Rules Committee approved a closed rule for the debate, allowing no amendments, and made minor adjustments to the bill. A vote on final passage is not expected until Friday.

As of Wednesday, Democratic leaders still had not locked down the votes to assure a majority.

“We’re closer today than we were yesterday,” said Majority Leader Steny H. Hoyer, D-Md., confirming reports from leadership aides that at least two more Democrats had converted from “no” to “yes.”

The $124.3 billion measure exceeds the president’s fiscal 2007 supplemental request by $21.3 billion. It contains spending for the wars in Iraq and Afghanistan, as well as for domestic priorities such as agriculture disaster relief and children’s health insurance.

The most controversial provision, though, would require withdrawal of most U.S. forces from Iraq as soon as the end of 2007, but no later than the end of August 2008.

The Senate Appropriations Committee on Thursday will mark up its version of the supplemental, which is expected to call for $121.6 billion in spending and include a provision similar to a previously defeated resolution (S J Res 9) that would require the start of a troop withdrawal from Iraq and set a goal for completing the process by March 2008.

The House Rules Committee early Thursday approved four hours of general debate for the measure.

House Republican leaders, along with Appropriations ranking member Jerry Lewis, R-Calif., and relevant authorizing committee ranking members had written to House Speaker Nancy Pelosi, D-Calif., requesting that Democrats allow amendments to be offered on the floor.

“We believe that an open rule for consideration of the supplemental is the only way the House should debate this binding bill. The war spending bill presents an appropriate opportunity for the Democratic leadership to fulfill its commitment by affording all members the opportunity to amend the bill, and we hereby request that you do so,” they wrote.

Republicans have said that appropriations bills are typically considered under open rules. For example, the four stand-alone war supplementals considered in the 108th and 109th Congresses were considered under open rules.

But Democratic Rules Committee spokesman John Santore said that during the 12 years of GOP House control, only seven of 15 supplemental appropriations bills were considered under open rules.

During the Rules Committee markup, Republican members questioned the addition of some domestic spending, such as $25 million for spinach farmers.

House Appropriations Chairman David R. Obey, D-Wis., defended the provision, noting that farmers had voluntarily recalled the spinach after an E. coli outbreak.

“This is people’s livelihood, and we’ve got every bit as much obligation to deal with domestic problems that interfere with people’s livelihood as we have to deal with some economic problem in Iraq,” Obey said.

Several Democrats said they had not yet made up their minds, including Indiana moderates Brad Ellsworth and Baron P. Hill and liberals Yvette D. Clarke of New York, Elijah E. Cummings of Maryland and Robert C. Scott of Virginia.

“I’m just going to take in all the information and make a decision when it gets right in my head,” Ellsworth said as he left a Democratic Caucus meeting. Lawmakers had just met behind closed doors for about an hour with Zbigniew Brzezinski, who served as national security adviser to President Jimmy Carter.

According to people in the caucus, Brzezinski told lawmakers, “If you don’t vote for this, you will send a message of confusion and give President Bush a free hand.”

A Democratic leadership aide called the speech “persuasive.”

Keith Ellison of Minnesota, another undecided Democrat, said, “When you’re dealing with issues of life and death, you can never completely close your mind, until it’s time to vote.”

Lynn Woolsey, D-Calif., who will vote against the supplemental, said that there is intense pressure on Democrats to vote for the measure.

Democrats received an endorsement of their proposal Wednesday when former Democratic Rep. Lee H. Hamilton of Indiana, co-chairman of the Iraq Study Group, wrote to Obey praising the bill for laying out benchmarks on the Iraqi government backed by conditional U.S. support, among other provisions.

“This resolution provides a light at the end of the tunnel. It is not perfect, but it moves our national debate forward,” Hamilton wrote.

Democrats can lose only 15 votes in their caucus and still maintain the 218 votes needed for a majority, unless they can pick up some GOP votes. Few House Republicans are expected to vote for the bill.

Wayne T. Gilchrest, R-Md., said he was leaning toward voting for the supplemental. He said he had the overall view that the military is “stunningly competent” and that General David H. Petraeus, the new top commander in Iraq, is “brilliant” but that they were expected to achieve victory by way of a flawed policy.

The House is not the best entity to direct a war, Gilchrest said, but the troop withdrawal language would send an important signal, even if Bush vetoes the bill and the final product ultimately does not include a timetable for troop withdrawal.

“The American people will hear it, the Iraqis will hear it, the Middle East will hear it,” Gilchrest said.

House Republicans say most of their conference is expected to oppose the bill. Chief Deputy Whip Eric Cantor, R-Va., would not specify the number of GOP defectors they anticipate.

“It will be a lot fewer than the 17” who voted with Democrats on a non-binding resolution expressing opposition to the troop surge, Cantor said.

House Republicans have boasted of being 99 percent unified in opposing the supplemental. Besides Gilchrest, another GOP House member known to be considering voting for the bill is Walter B. Jones of North Carolina.

Susan Ferrechio, Jonathan Allen and John M. Donnelly contributed to this story.