By Richard Cowan and Susan Cornwell WASHINGTON, March 15 (Reuters) - A Democratic plan to withdraw American combat troops from Iraq by next year passed a key test in the U.S. House of Representatives on Thursday, but the Senate failed to impose a similar deadline for ending the 4-year-old war. On a mostly partisan 36-28 vote, the House Appropriations Committee approved a $124.1 billion emergency spending bill, including $95.5 billion to continue fighting wars in Iraq and Afghanistan this year. The legislation, which could be debated in the full House as early as next week, would set strict conditions on continuing the Iraq war for the next 18 months and would end U.S. combat there by Sept. 1, 2008. The White House has threatened a presidential veto of the measure, which first faces tough going in the Senate. "We are trying to deliver a message to the politicians in Iraq that we are not going to sit around forever watching them dither, watching them refuse to compromise, while our troops die," House Appropriations Committee Chairman David Obey, a Wisconsin Democrat, said as his panel began a sometimes-heated debate on the war. The legislation marked the first time a congressional committee voted to put binding limits on the duration of the 4-year-old war in Iraq. As the House panel voted, the Senate wrangled over a separate Democratic resolution encouraging President George W. Bush to bring U.S. troops home by March 31, 2008. That measure failed on a 50-48 vote in which 60 votes were needed for passage, but anti-war senators may try again in the spending measure. "This is a process. Step by step, we're moving towards having our soldiers, sailors, and Marines return home from Iraq. That is what this is all about," Senate Majority Leader Harry Reid, a Nevada Democrat, told reporters before the vote. Even if congressional Democrats fail to enact legislation to end the increasingly unpopular war, they are hoping to accomplish two things -- to deliver on last year's campaign promise that they would try to bring the troops home and to apply pressure on the Iraqi government to take more responsibility for security, a goal Bush also seeks. "This is a civil war and the Iraqis have to take this up themselves," said Rep. John Murtha, the Pennsylvania Democrat who says the war is ruining U.S. military capability and began calling for a withdrawal from Iraq in November, 2005. Congress hopes to finish work on the war-spending bill by next month, when the Pentagon says it will run out of money to wage war. Next week, the Senate Appropriations Committee will write its version of the war-spending bill and it was not yet clear what conditions the panel might impose on the money. But Chairman Robert Byrd, a West Virginia Democrat, said on Wednesday, "The Congress of the United States will not support an unaccountable, open-ended war in Iraq." Rep. Jerry Lewis of California, the senior Republican on the House Appropriations Committee, countered that a timetable for withdrawal "will signal to the insurgents that the United States does not have the political will to support this fledgling democracy." The Democratic plan would "tie the hands of our commander-in-chief at a time of war," Lewis said. The only Democrat on the House committee to vote against the bill was Rep. Barbara Lee, a California Democrat, who wants to end the war this year. Next week's vote in the full House is expected to be close. A House Democratic leadership aide said it was encouraging that two liberals and one conservative on the appropriations panel, who had been leaning against supporting the bill, ended up voting for it. To entice wavering lawmakers to vote for the bill, House Democrats have included $6.4 billion, significantly more than Bush sought, in new money to help southern states rebuild after devastating hurricanes in 2005.