It's midday on the corner of N and 14th streets NW: Construction crews are at work on a gutted building, teenagers mill around on the sidewalk and Deborah Maiese is counting doorbells.

She stands in an entryway and runs her finger down the directory of tenants, counting two by two, then rings the office to ask about unlisted apartments. Is there a unit for the custodian? For the resident manager?

An angry, disembodied voice screams out from the little metal box: "I have been over this with the Census Bureau for two dozen times!"

Maiese smiles and shrugs, unfazed. Counting households is harder than it looks.

Maiese, research manager for the District's Office of Policy and Program Evaluation, has spent the last two weeks looking for homes the Census Bureau missed in its national head count this spring. It is a process that has been going on across the country, with nearly 6,300 local jurisdictions challenging what they say were the unrealistically low preliminary population totals released in late August.

In the midst of charges that the 1990 census has been seriously flawed, the fate of these challenges -- the bureau has said it will go over the discrepancies and, if necessary, send out workers to recount -- could be critical in resolving the ongoing debate about whether the head count is overlooking huge numbers of people and households.

For local and state governments, the controversy revolves around very real concerns: the federal dollars and political representation that will be linked for the next decade to the bureau's figures.

In the District, where the early numbers show population dropping 10 percent to 574,844, officials vowed to find people and homes missed by census workers.

But arriving at a precise number of households, said Maiese, "is intrinsically difficult."

She has been paging through tax records, voter registration rolls and building permits, looking for homes that may have been omitted from census lists. And she has walked the streets, taking note of mailboxes, utility meters and trash cans, anything that might give a clue to how many units are contained within.

Her purpose is not to count heads, but households, the basis on which local governments must contest the early census findings. Next year, the bureau will release final population totals, revised in large part as a result of these challenges.

"People look at me like I'm crazy: Why can't you just count?" Maiese said. She ticks off the reasons: illegal basement units, garage apartments, businesses that double as homes, a gutted apartment building where the units must still be tallied.

Say there's a row of four-story brownstones. Some have multiple utility meters. Some have multiple buzzers. One doesn't. Is it a single-family home, or has the landlord put the mailboxes inside because subdivision is illegal? You can knock on the door, but often there is no answer. Is it vacant?

"It is complex," said Maiese. "I guess we could be empathetic with the Census Bureau."

Though the bureau has a larger crew to canvass the streets, local governments feel that they have better administrative records, as well as local knowledge. And on some of Washington's "mean streets," said Maiese, it's very possible census workers chose not to get out of their cars or pound on doors.

Nevertheless, District officials say they will argue in an official challenge to be filed today that 5,000 housing units were bypassed by the census, a figure that translates into roughly 11,000 people.

An additional 10,000 residents living in group quarters were missed, the District contends, pointing to an American University dormitory and more than 1,000 residents of the Soldiers and Airmen's Home that were not included in bureau totals.

"It's an inexact science," said Peter Hartjens, director of policy and program evaluation for the District. Though the Census Bureau has been "quite cooperative," he said, "we still think they've missed gobs and gobs of people, large numbers of Hispanics and homeless."

The District is not alone in finding large discrepancies.

New York City said last week that the bureau had failed to count 254,534 residents, missing at least five housing units on 43 percent of the city's 28,000 blocks.

Chicago officials found problems on half of the city's 22,000 blocks. Detroit cited problems on virtually all of its 13,000 blocks. Houston said the bureau missed 32,000 households and Los Angeles cited 50,000 housing units not included on the bureau's lists.

"These people are all saying the same thing: It's a mess," said Lance Simmens, assistant executive director of the U.S. Conference of Mayors.

But Census Bureau Director Barbara Everitt Bryant has repeatedly told Congress that the head count is on track. Though census officials cannot speculate how the numbers will change as a result of the challenges, they expect that, in virtually every jurisdiction, the numbers will rise.

And bureau officials have argued that the challenges, though important in arriving at a final number, are not proof that the census has failed.

By Friday, three days before the deadline, 6,294 local jurisdictions, out of a total of 39,276, had filed challenges. That leaves nearly 33,000 jurisdictions that had not contested the preliminary figures.

"That's a significant number . . . who basically are saying the numbers are good," said bureau spokeswoman Deirdre Blackwood.

District officials say much is at stake, arguing that the city lost as much as $265 million in federal funds over the 1980s because the census missed between 5.8 percent and 12 percent of its residents.

In preparation for the 1990 challenge, city officials compiled an address register, using a list purchased from a commercial advertising firm and supplementing it with administrative files, including property tax, voter registration, public assistance, apartment building licensure and utility records.

Using their list, District officials found 470 blocks on which they believed there were at least five households more than shown on the preliminary census results. Much of the discrepancy they documented with records.

But on 28 blocks, where there was a difference of at least 50 units, city workers went out to count for themselves.

Even going door to door can be confusing. Take Census Track 52.01, Block 111: the Northwest block running from 14th Street, along N Street, up 15th Street and back toward 14th on Rhode Island Avenue.

Maiese starts with the apartment building at 14th and N streets, where she was greeted by the voice of the exasperated manager. That totals 152 units.

But then it gets complicated. Next-door is a three-story brick house. There are eight mailboxes, two without names. Are there more units in the basement? She counts it as eight.

Next-door is another apartment building. The permit in the lobby says 84 units, but there are only 67 names listed. Maiese calls the manager. Total is 84.

Then there is a gutted apartment building under renovation, which still must be counted in the housing unit total.

"There is a classic example," Maiese said, waving her arm at the nine-story building, where there are no internal walls to help determine the number of apartments. "You tell me how many apartments there are."

Ultimately, Maiese called upon city records, found that the building was public housing for the elderly and had been damaged by an explosion but would eventually reopen. The unit count, according to records, was 151 units, mostly efficiencies.

Without the records, one could easily have guessed there were fewer than 50 units.

As she continues around the block, Maiese comes upon a boarded-up, padlocked building. She estimates 14 units by comparing the size to a similar, occupied building next door.

Then there are two buildings that look like single-family homes, but one has six trash cans in front. Maiese counts each as one unit.

When she visited an apartment building facing 15th Street, the property manager said there were 214 units, but the license said 209 units and there were only 207 buzzers. She counts it as 209.

Around the corner on Rhode Island Avenue is a hotel used by the city as an emergency shelter. Maiese can use city records to count units there, but she points out that a census enumerator could easily have assumed that it was a traditional hotel and skipped it altogether.

Down the block there is a building that looks like it may hold an art gallery, but there are four buzzers, two taped over. The door is locked. Maiese is stymied on this one.

Then there is a complex with a sign advertising nine town houses with efficiency units, but there are 12 mailboxes at the door. She counts 12.

"It makes me appreciate the complexity of this," Maiese said.

Initially, the city believed the Census Bureau was at least 50 units short for the block. But after Maiese's count, the city logs in 752 units, 34 more than the bureau had found.

At the bureau's regional office in Charlotte, N.C., which has jurisdiction over the District, director William F. Hill is calm about the challenges he must study over the coming weeks.

"We've already found some of that," he said, citing as an example a university dorm in the District that had been miscoded in the preliminary numbers. "The truth of the matter is, we miss some things. I don't know how."

Though he said he expected little problem resolving the District's challenge, he said some of the cities that had cited huge discrepancies were probably using flawed records.

"Did we miss 25 percent of the housing units in some big city? I doubt it."