NEW YORK — Sheila Birnbaum is known in legal circles across New York as the "queen of torts" for her prowess in sorting out complicated cases. But she may be up against her most daunting task to date.

Since Attorney General Eric Holder appointed her special master of a Sept. 11 victims' compensation fund in May 2011, Birnbaum has been responsible for evenhandedly distributing $2.7 billion to ground zero responders and others who became ill after being exposed to dust and ash from the smoldering ruins of the World Trade Center.

The problem is, she doesn't quite know how many people will be eligible for compensation.

"We haven't yet received the avalanche of claims that might have been expected," she said, noting that only about 300 people have filed eligibility forms so far. The fund will ultimately receive thousands of applications, she predicts.

Nearly two years after President Barack Obama signed the James Zadroga 9/11 Health and Compensation Act into law, about 40,000 responders and survivors receive monitoring and 20,000 get treatment for illnesses as part of the World Trade Center Health Program – one of the law's two components. But the other, Birnbaum's fund compensating the same kind of people for economic losses, hasn't been as quick to get off the ground.

It's not a matter of bureaucratic foot-dragging, but rather an illustration of the complexities of key legislation born of the attacks that took place 11 years ago next week.

"This is a lot more complicated than meets the eye," said Birnbaum, an attorney.

With time still left to submit claims, some people are holding out in the event that they become sick in the near future. Others are waiting until the National Institute for Occupational Safety and Health officially adds 14 broad categories of cancer to the list of conditions covered by the fund.

The national institute's director, Dr. John Howard, said in June that it planned to expand coverage to include scores of cancer types. An institute spokeswoman would not give a specific date for the announcement, although Birnbaum said she anticipates it this month.

Recently diagnosed with leukemia and lymphoma, 55-year-old Brian Casse hopes he can secure money from the fund to support his wife and children in case he takes a turn for the worst. Casse, a retired firefighter who helped clear away the mountain of rubble at ground zero, believes there's little doubt his work at the site is responsible for his illness.

"You've got people in this city who went down there and did what we had to do. And a lot of us got sick because of it," Casse said. "To make us now fight for this money, it's not right. In the grand scheme of things, this money's a drop in the bucket."

Initially, the Zadroga Act – named for police Detective James Zadroga, who died at age 34 after working at ground zero – included only a short list of illnesses that qualified for compensation. Cancer was excluded because of a lack of scientific evidence linking any form of the disease to conditions in the debris pile.

"To me, it's common sense. If you breathe in toxic fumes, you're going to get cancer," said U.S. Rep. Carolyn Maloney, a Manhattan Democrat who helped author the bill.

But even Maloney conceded that it is difficult to find hard data proving the connection between cancer and the dust at ground zero. That's why in crafting the Zadroga Act, lawmakers were careful to include mechanisms that would allow for illnesses to be added based on new scientific research.

An inclusion of cancer on the list will likely encourage more people to file claims. Applicants will have to provide evidence of their diagnosis and time spent at ground zero, though they do not need to enroll in the health program to receive compensation. Birnbaum's staff, which includes 50 people but is expected to grow, will then determine whether claimants are eligible.

The fund has $875 million to distribute in its first five years. The rest of the money will become available in its sixth year, so that recipients will get their awards in two payments.

"If people's expectations were that they were going to get a whole bunch of money immediately, that's not the way the fund was set up," she said. "We're going to do this in a fair and transparent way."

It's a tricky job, especially considering that Birnbaum assumed her role with no structure in place. In just a few months, her team had to write up legal documents, set up computer programs to analyze claims and launch an operation that would distribute the funds equitably.

"There was no structure, there was no office, there were no computers, no employees. Everything had to be created from scratch," said Birnbaum, widely considered one of the city's top lawyers. She declined to be paid her work with the fund.

Birnbaum acknowledges she can't afford any mistakes. If Congress isn't happy with how she handles the distribution, the fund risks losing political support when advocates push for reauthorization after 2016.

The fund, which Congress originally established in 2001 to prevent potentially devastating class-action lawsuits against the airlines whose planes were hijacked and used in the 9/11 attacks, gave $6 billion to the families of victims and $1 billion to the injured.

When it closed in 2003, however, those whose injuries materialized years later were left without the ability to benefit. That group included workers and volunteers, many suffering from chronic respiratory problems after being exposed to clouds of pulverized building materials at the site.

On Dec. 22, 2010, in a last-minute compromise during the final hours of its legislative session, Congress reopened the fund when it passed the $4.2 billion Zadroga Act.

In the run-up to the Zadroga Act's passage, some fiscally conservative Republican lawmakers were reluctant to support the bill, citing concerns over the cost of a multibillion-dollar entitlement program.

Sen. Tom Coburn, R-Okla., led the charge on a Republican filibuster before striking a deal with Democrats to reduce the package by $2 billion. It won unanimous consent in the Senate, and the House approved it hours later.

Advocates say they are mindful of how difficult the process was in 2010 when looking ahead to possible reauthorization.

"A lot of people who live west of the Hudson River believe this is New York City's problem and that we're just looking for a government handout," said Michael Barasch, a lawyer whose firm is representing 5,500 first responders and residents who lived near the site. "If these people take control of our government, there certainly won't be any additional funding."

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