The A.F.L.-C.I.O.’s leaders voted overwhelmingly on Thursday to endorse Barack Obama for president, saying the federation would spend more than $50 million and deploy more than 250,000 volunteers in this fall’s campaign. John J. Sweeney, the federation’s president, said, “Barack Obama’s record demonstrates he is a champion for working families and his proposals will improve life for generations of working people and our children.