Washington (CNN) -- A health care bill meant to provide free medical treatment to those suffering from the health effects of working in and near ground zero following the 2001 attacks may come up for a Senate vote on Wednesday.
Sen. Charles Schumer, D-New York, said it appeared the bill will come up for a Senate vote once lawmakers vote on the START treaty, a nuclear arms control pact with Russia and a top foreign policy priority of President Barack Obama.
"It will be decision day in the Senate, and we will see once and for all who will keep their promise to never forget the heroes of 9/11," Schumer said Tuesday.
The James Zadroga 9/11 Health Bill is named after a deceased New York Police Department detective who had worked in the toxic plume at ground zero.
The House had passed the previous bill on a mostly partisan 268-160 vote.
The amended version of the Senate bill shrinks the $7.4 billion price tag that prompted Republican opposition, and now costs $6.2 billion over a 10-year period, following a court settlement that benefited some of the responders.
Its advocates boast that the bill is funded by a procurement fee on some foreign countries that trade with the United States, the continuation of a fee on some travelers to the United States and a fee on visas for some companies.
If passed by the Senate, the bill would return to House lawmakers for approval before President Barack Obama could sign it into law.
On Tuesday, a group of 9/11 first responders joined lawmakers in Washington to urge the Senate to pass the health care bill.
"Fourteen of our guys died that day and we continue to see our friends die on a day-to-day basis," said Glen Klein, a New York police officer who said he is sick with lung disease. "We're asking for the right to live."
In the years following the attacks, health experts have noted respiratory and mental health conditions, such as post-traumatic stress disorder, in those who engaged in ground zero rescue and cleanup efforts.
"Apparently we have some senators who would like to believe that when 343 fire officers and firefighters [and thousands of civilians and police officers] died on 9/11...that was the end of it," said Steve Cassidy, president of the Uniformed Firefighters Association.
"If that were true, we could move on."
The bill has been in legislative limbo since Thursday, when Senate Democrats failed to win a procedural vote to open debate on it.
But on Sunday, Democrats said they were hopeful they had pulled off "a Christmas miracle" by changing the bill enough to garner Republican support.
CNN's Dana Bash contributed to this report.