The fund is projected to be depleted at the end of 2020.
“We will reach the point soon, most likely this year,” Senator Chuck Schumer of New York said this month, “when more will have died from 9/11-related illnesses than on 9/11 itself.”
So far, about 21,000 claimants have received some $5 billion. An additional 19,000 or so claims are pending.
To redeem new claims and prevent reductions in prior ones, the House Judiciary Committee endorsed the bill sponsored by Representatives Peter T. King, Republican of Long Island, and Carolyn Maloney, Democrat of Manhattan, to extend the fund for decades. The full House is expected to do so next month.
“I did not want to be anywhere else but ground zero when I was there,” Mr. Alvarez told Congress. He added, though: “Now the 9/11 illnesses have taken many of us, and we are all worried about our children, our spouses and our families and what happens if we are not here.”
On June 26, when emergency medical workers met with Mr. McConnell, one man clasped the senator’s hand; when that man, John Feal, a demolition supervisor who lost part of his foot in an accident at ground zero, released his grip, the senator was holding Mr. Alvarez’s New York City police badge.
“For a New York City police officer to give up his badge, that’s like somebody donating an organ,” Mr. Feal later told CNN, “and Luis wanted the Senate majority leader to understand the importance of this, and to be reminded that people are sick and dying.”