The city is overseeing the cleanup effort, sending in cleaners in hazmat suits, gutting basements and replacing boilers and hot water heaters. The city’s Department of Health and Mental Hygiene is conducting air quality tests, and the comptroller’s office is helping people file claims. And the D.E.P. is currently pumping more than 10 million gallons of wastewater into sewers that are not affected by the blockage.

Many families have not been reimbursed yet for any expenses they have incurred, because legally the city requires them to file a claim first.

Those expenses, for most residents, are running to tens of thousands of dollars. Many people who have been forced out of their homes, or need to buy new beds, refrigerators and winter clothes, must pay out of pocket or wait until the city approves their claims.

Supreet Singh, 36, who lives with her husband and 2-year-old daughter, said her family had to put about $5,000 on credit cards to cover cleanup equipment before the city provided assistance. They have not been reimbursed.

“It’s not like we have the cash to go out and buy stuff, which is what angers a lot of people,” Ms. Singh said. “Every one of us is working hard.”

Scott Stringer, the city’s comptroller, said his office is committed to reviewing claims quickly. The comptroller’s office is also allowing people who have suffered damages to submit an estimate, which expedites the process.

“We want residents to know that we’re going to do everything in our power to help them,” Mr. Stringer said.