New York (CNN) -- New York Mayor Michael Bloomberg joined lawmakers, police and fire officials on Monday in urging U.S. Senate passage of a health care bill benefiting September 11 rescue workers.

"The time for excuses is over," Bloomberg said. "The Senate has a full week ahead of it and should not adjourn until it passes this bill."

Bloomberg said the measure is paid for by "other revenue generators," referencing 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.

"There are men and women dying today," said Republican Rep. Peter King, who stood beside Bloomberg during Monday's news conference. "We are absolutely obligated to pass this bill for them."

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, the Democrats said they were hopeful they had pulled off "a Christmas miracle" by changing the bill enough to garner Republican support.

The James Zadroga 9/11 Health Bill -- named after a deceased New York Police Department detective who had worked in the toxic plume at ground zero -- seeks to provide free medical coverage for responders and survivors who were exposed to toxins after the attacks.

Joseph Zadroga, father of the bill's namesake, asked lawmakers Monday to pass the measure so that first responders now suffering from working in the toxic conditions can "go on with their lives with dignity and honor."

In the years after the 2001 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.

The House has passed the bill on a mostly partisan 268-160 vote.

Bloomberg had called Thursday's result "a tragic example of partisan politics trumping patriotism."

Republicans complained that the $7.4 billion price tag was too high, while Democrats said the government had an obligation to help the first responders in the deadliest terrorism attack in U.S. history.

On Sunday, a longtime champion of the bill, Sen. Charles Schumer of New York, said Democrats had retooled the measure to gain Republican support.

"Barring a setback, we believe we're on the path to victory by the end of this week," he said.

Kirsten Gillibrand, D-New York, called the announcement "a Christmas miracle" for the bill, noting that its sponsors changed the way the fund would be paid for and cut its total cost in response to Republican concerns.

Instead of coming with a $7.4 billion price tag, the bill will now cost $6.2 billion over 10 years, after a court settlement that benefited some of the responders.

If passed by the Senate, the bill would return to House lawmakers for approval before President Barack Obama could sign it into law.

Senators have a long to-do list to finish before breaking for Christmas. In addition to resolving the debate over the START treaty, they need to pass a funding bill that would keep the federal government running into 2011.

CNN's Steve Kastenbaum, Rachel Streitfeld and Raelyn Johnson contributed to this report.