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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.”