The program created by Congress had authorized $5.9 billion in payments as of Monday afternoon, with payments ranging from $500 to $8.6 million.
Fund administrators have determined awards for 2,454 out of 2,963 death claims, and 2,449 injury claims out of about 4,400. The vast majority of injury claims are for lung-related ailments from those who worked in rescue and recovery operations at the World Trade Center site.
Close to 2,000 injury claims are expected to be rejected or withdrawn due to insufficient medical proof of injuries.
Fund workers still have hundreds of claims to finalize before their congressionally imposed Tuesday deadline, said Kenneth Feinberg, the special master overseeing the fund.
"We will be working right up until midnight," he said.
Once the deadline passes, officials expect it will take about eight to 10 weeks to get all of the checks mailed out.
The average death payment is just above $2 million, while the largest death payment to date has been $7.1 million.
Among injury claims, the largest payout has been $8.6 million for a woman crushed by debris at the World Trade Center, and the smallest $500.
After a rocky start, the fund is largely judged a success.
"It had all the ingredients in the world of a monumental failure, and instead it has been an extraordinary program," said John Bailey, executive director of Trial Lawyers Care, a group that coordinated free legal services for applicants to the fund.
Bailey credited the success to families, their lawyers, and fund administrators agreeing to work together after some particularly bitter criticism, much of it directed at Feinberg.
"At the start, people were exceedingly angry, and they were looking for a bogeyman, and Ken Feinberg was there — but his heart has always been in the right place," Bailey said.
Most families seem to agree, though about 100 lawsuits are going forward claiming negligence against U.S. companies for failing to prevent the attacks.
"I was against the fund in the beginning... but now I honestly believe it was a success," said Bill Doyle, whose son Joseph was killed in Tower 1 of the World Trade Center. Doyle has since filed a claim with the fund and coordinated an information-sharing program with other Sept. 11 families.
The fund was created to protect the airlines and U.S. entities from possibly crippling litigation, while compensating those killed or injured in the attacks.
It was met with fierce criticism by the families, who considered the initial monetary estimates too low. Many also were offended that the government had created a formula to place widely different dollar values on different victims based on their expected annual income.
The opposition softened as lawyers argued many of those award amounts upward, and ultimately, foregoing the chance to sue airlines and security companies for alleged negligence.
Feinberg said Congress should take a hard look at whether it should ever again agree to create such a program, especially one that puts different cash values on lives.
After listening to hours and hours of wrenching testimony from survivors and the families of the nearly 3,000 people killed, Feinberg said he has become "much more fatalistic about life and death."
"I'm not sure it makes much sense to predict what you want to do two weeks ahead of time," Feinberg said. "Life has a way of throwing curveballs; I think the courage of these families has been overwhelming."
By Devlin Barrett