On Nov. 9, 2012, less than two weeks after Hurricane Sandy made landfall, Kenneth G. Langone pulled on a pair of construction worker's bright yellow galoshes and accompanied Senator Charles E. Schumer and other officials through a foul-smelling mix of diesel oil and water in the basement of his namesake, NYU Langone Medical Center. By early 2013, Mr. Schumer and his Senate and House colleagues had approved $60 billion in post-hurricane disaster aid, with a large chunk destined for NYU Langone. Mr. Langone, the co-founder of Home Depot and a major hospital benefactor, has been returning the favor.