House Democratic leaders agreed to bring the bill to a vote after Congress returns next week from its summer break, U.S. Reps. Carolyn Maloney and Jerrold Nadler said.
The bill would provide free health care and compensation to 9/11 rescue and recovery workers who fell ill after working in the trade center ruins.
In July, thethat was needed under the procedure that Democratic leaders used to bring up the bill to block potential amendments. The bill fell short, 255-159. The vote was largely along party lines, with 12 Republicans joining Democrats supporting the measure.
Maloney and Nadler said that this time, the bill will need only a simple majority.
Maloney and Nadler said they are approaching the vote "with the expectation and belief that neither side will play politics with this vitally important legislation."
The July vote sparked an angry exchange between two New York congressmen, Republican Peter King and Democrat Anthony Weiner.
During floor debate before the vote,, a Long Island Republican.
"The gentleman is providing cover for his colleagues rather than doing the right thing," bellowed Weiner, who represents parts of Brooklyn and Queens. "Republicans wrapping their arms around Republicans rather than doing the right thing on behalf of heroes. It's a shame, a shame."
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King, a key backer of the bill, had accused Democrats earlier of staging a "charade."
The harsh words were sparked by the decision by Democratic leaders to use the procedure that required the two-thirds majority vote.
King said Democrats were "petrified" about casting votes on amendments, possibly including one that would ban aid from going to illegal immigrants sickened by trade center dust.
King's comments angered New York Democrats, who blamed Republicans for not supporting the bill and accused King of not doing enough to win more GOP support for the measure.
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.
Members of Congress from New York and New Jersey have been pushing such a measure for years.
Similar legislation is pending in the Senate.