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The bill would be paid for with a fee on some foreign firms that get U.S. government procurement contracts. The bill also calls for extending fees on certain firms that rely on H-1B and L-1 visas.

The legislation is named for James Zadroga, a police detective who died at age 34. His supporters say he died from respiratory disease contracted at ground zero, but New York City’s medical examiner said Zadroga’s lung condition was caused by prescription-drug abuse.