NEW YORK — Facing Superstorm Sandy’s daunting toll of wreckage and displacement in the nation’s largest city, officials have put much of their hopes and hundreds of millions of dollars into jump-starting repairs to make homes livable.

Federal and city officials see the strategy — focusing on getting people back into their own homes, not temporary housing — as an innovative and nimble answer to the challenge of housing thousands of storm victims in a notoriously expensive and crowded area.

But with relatively few homes fixed so far, questions are emerging about whether the “rapid repairs” initiative can live up to its name.

More than 10,000 homeowners have signed up for NYC Rapid Repairs in the three weeks since Mayor Michael Bloomberg launched the initiative to bring in hundreds of contractors to restore power, heat and other essentials free of charge.

Contractors have done initial assessments of about 7,000 homes in the city and 2,000 in similar initiatives on Long Island, but just about 400 projects have been completed so far.

Officials stress that they’re still ramping up the program. But a community meeting last week in hard-hit Staten Island boiled over with complaints that repairs and other aid aren’t coming fast enough, a familiar refrain in storm-damaged areas.

Noreen Connolly-Skammel’s home on the Rockaway peninsula in Queens was hit by a basement fire and then a flood that swamped the cellar and two feet of the first floor. She said the NYC Rapid Repairs program was swift at first, conducting an assessment within two to three days after her call. But she heard nothing further for about two weeks, when she was told a new assessment had to be done.

Anxious to get the work going, she and her husband spent about $8,300 of their own money on boiler, hot water and electrical repairs — the very sort the government program might have done for free.

“I wish they were a little more rapid,” she said, noting that the program has since pledged to help with other repairs.

Officials are asking for patience with the first-of-its-kind effort.

“We are moving as quickly as we can on these repairs,” Michael Byrne, the Federal Emergency Management Agency official supervising Sandy recovery in New York state, said in a statement Monday.

FEMA is paying much of the bill for the home-repair program, while also subsidizing hotel stays and apartments for thousands of Sandy victims — help some say has come promptly, but not without snags.

For FEMA, Sandy represents one of the biggest tests since Hurricanes Katrina and Rita in 2005 rendered 300,000 homes uninhabitable along the Gulf Coast, displaced more than 1 million people and spurred a national examination of disaster housing.

Citing the confusing and problem-plagued process of housing people after Katrina, FEMA’s 2009 National Disaster Housing Strategy calls for improvements from exploring new forms of temporary housing to providing more social services to the displaced.

Yet city, state and federal officials didn’t have a ready answer when they realized that as many as 40,000 city residents might need temporary quarters after Sandy, an estimate that quickly shrank as many homes got heat and electricity back.

Byrne says he feels FEMA — which has OK’d more than $673 million in housing and home-repair aid so far in New York alone — has at least gotten a handle on the disaster. But “my job is to always feel like I’m missing something,” he said.

More than a month after the Oct. 29 storm, the need for housing is a moving target that hangs on day-to-day developments for thousands of people.

Roughly 6,700 buildings around the city require significant repairs to be habitable, and about 750 more are deemed structurally unsound, according to city Buildings Department statistics. And in one measure of the demand for help, about 2,100 households are in FEMA-paid hotel rooms. Some storm victims also have gotten money for apartment rentals; a number isn’t immediately available.

With her first child due on Christmas Eve, Corinna Sabatacos and fiance Steven Ferrara had to move out of their severely damaged Rockaway house. They say they ended up in a hotel that doesn’t take FEMA payments and have gotten conflicting answers on whether the more than $2,000 bill will be covered.

“Things just change daily, and that’s what’s so frustrating,” Sabatacos  said. The couple expects to move this week  into an apartment, aided by a $1,200-a-month FEMA rent subsidy.

As displacement and uncertainty continue, some officials recently broached a tried but controversial approach — trailers, a housing standby for FEMA in many disasters.

But Byrne sees them as an unpromising option in a densely packed city, especially since some of the open spaces suggested for a trailer encampment are in flood zones.

By hastening repairs, officials hope instead to solve the temporary housing crunch by shrinking it.

It’s not uncommon for FEMA to pay for crucial fixes, such as replacing a furnace or fixing a flood-damaged electrical system. But usually, the agency assesses the damage and insurance and gives homeowners a check, leaving them to arrange the work.

FEMA and city officials reasoned they could get homes fixed faster if the city hired contractors, coordinated repair requests, dispatched the workers and paid for it all directly. The free repairs come on top of the $31,900-per-family cap for FEMA aid.

The city has agreed to spend $500 million on the effort; FEMA is to repay at least 75 percent. Long Island’s Nassau and Suffolk counties have similar, but so far smaller, initiatives. A program like rapid repairs is not taking place in New Jersey as of now, but FEMA officials there say they are looking at a number of options for the state.

About a half-dozen NYC Rapid Repairs workers were busy last week in Stephen Murray’s gutted Staten Island home, its windows about five feet off the floor speckled with debris. The line marks how high the water rose as Murray fled Sandy in a neighbor’s pickup truck.

The workers expected to spend several days  replacing the flood-damaged wiring, furnace and hot water heater and putting down plywood where sodden floors were ripped out — not restoring the home completely, but making it safe. Murray and his wife are living in an apartment in the meantime, with FEMA’s help.

Both retired after workplace injuries; they couldn’t afford flood insurance or the $60,000 estimate to repair the two-bedroom bungalow. But he figures the city repairs, FEMA aid and elbow grease from friends and family should be enough.

“If the city didn’t come in here and help me, I don’t know what I would have done,” Murray said.

As he spoke, a light bulb flicked on overhead, a sign that the workers had restored the home’s connection to the power grid.

“Oh, man,” Murray said. “You have no idea what it feels like.”