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Updated: 6:39 p.m.The House sent a stripped-down $60 billion supplemental war spending bill to the president for his signature Tuesday, after Senate Majority Leader Harry Reid (D-Nev.) demonstrated last week that his chamber had no appetite for a broader measure.The fiscal 2010 war supplemental bill was cleared with the help of Republicans, 308-114. House Minority Whip Eric Cantor (Va.) said earlier Tuesday that Republicans would support the measure and 160 voted in favor, with 12 against.House Appropriations Chairman David Obey (Wis.) was one of 102 Democrats to oppose the bill. He brought the supplemental to the floor but said Tuesday that he would vote against it because of the high cost of the war in Afghanistan and his doubts about the Afghan governments abilities.The Senate rejected a broad war supplemental from the House on Thursday, then sent Members the narrow bill without funding for teachers, border security and other items sought by House Democrats.Steven T. Dennis and John Stanton contributed to this report.