Nadler said House Speaker Nancy Pelosi (D-Calif.) supports the bill. Another supporter, Rep. Peter King (R-Seaford), said some Republicans would vote for it.

King said the House could pass it as soon as May or June. But Maloney said in a statement later she hoped for passage "by the eighth anniversary of the attacks" on Sept. 11, 2009.

Noting that President Barack Obama said he supported the bill when running for president last year, Nadler and Maloney said the bill's fate would then lie in the Senate.

They said Sen. Charles Schumer (D-N.Y.) has said he would introduce a companion bill as its original backer, Hillary Rodham Clinton, has left the Senate.

Schumer, who came in for some barbed comments at the hearing for not pushing the bill, issued a statement saying he'll ask Clinton's replacement, Sen. Kirsten Gillibrand, to share responsibility for the bill.

"We're very concerned about the health of the 9/11 workers, and we're working with Senator Gillibrand on the best way to help them," it said.

Thousands of workers connected to Ground Zero became ill after the Victims' Compensation Fund for 9/11 workers stopped taking claims in 2003 and they now seek compensation and health care costs.

About 11,000 of them are suing the city and contractors, witnesses said. A $1-billion fund Congress set up has spent $350,000 on claims - and $200 million to challenge the claims.

The bill, which would reopen the fund and limit contractors' liability, would send an important signal so that workers and contractors will not be reluctant to respond to any future attacks or disasters, backers of the legislation said.

The bill also represents the best hope for those who are ailing and for the city, both of which are tied up in lengthy litigation, said New York City Corporation Counsel Michael Cordozo. There will be no winners in the litigation, he said.