Bags of potatoes and other groceries clutter the kitchen floor of the apartment Dionicia Gomez and her two sons share with a married couple. A bathroom medicine cabinet is stuffed full, and the Gomezes’ bedroom overflows with clothes, toiletries and three beds.

“This is what one must do in order to provide a home for your children,” said Gomez, whose apartment is part of a bustling complex that overlooks a golf course outside Falls Church. “There are a lot of people in this area living the same way.”

Fairfax County has struggled for years to find a way to address such overcrowding, with county inspectors repeatedly citing homes for having too many families living in them, and planners and lawmakers searching for ways to promote more modest, affordable housing in a community filled with spacious single-family homes and McMansions.

So far, it has been an uphill battle. The county Planning Commission is expected to recommend Wednesday that the Board of Supervisors stop considering a proposed amendment to zoning laws that would have fostered the creation of more studio apartments in Fairfax.

By allowing developers to build single-occupancy studios in various parts of the county, the “Residential Studio Unit” measure sought to address the influx of lower-income families to one of the country’s wealthiest suburbs while also creating more affordable housing for young professionals that Fairfax County is eager to attract.

Danery Lobo, left, and Henry Torres play in the bedroom of their Fairfax County apartment, which they and their mom, Dionicia Gomez, share with an unrelated couple. (Yue Wu/The Washington Post)

During months of often contentious debate, the amendment faced fierce resistance from homeowner groups that said they were worried about increased density. Planners have concluded that no acceptable compromise could be found.

The county now will seek new ways to create housing for lower-income families and young professionals, said Sharon Bulova (D), chairwoman of the Fairfax County Board of Supervisors and a proponent of the failed studio measure.

“I think we need to take a step back and have a broader discussion with the community about the need for affordable housing,” Bulova said. “This particular tool was not received well.”

Five years have passed since federal officials busted a mortgage fraud scheme in Fairfax County, exposing a host of unsafe living conditions among families crowded into basement apartments and converted houses that they could not individually afford.

So far this year, county inspectors have investigated 497 complaints of overcrowded housing, with about two-thirds of that number leading to citations, officials said. Last year, 814 homes were cited for overcrowding in places including Falls Church and Annandale. Homeowners complain that the problem is far more widespread than the number of citations would suggest, while housing advocates argue that the citations illustrate an increasing need for more affordable options.

“Overcrowding is really the market’s response to a lack of affordable housing,” said Michelle Krocker, executive director of the Northern Virginia Affordable Housing Alliance. “People don’t choose to live in overcrowded conditions. [But] if that’s the market, that’s what they do.”

A study published this month by the Urban Institute and Metropolitan Washington Council of Governments found that 24,500 of all renters in Fairfax pay more than half of their monthly income on rent.

During the last school year, 1,771 public school students in the county were in overcrowded living conditions, which can affect a child’s mental health and academic performance, Fairfax County school officials said.

The Rev. Kathleen Kline Moore, pastor of First Christian Church in Falls Church, said the shortage of affordable housing has taxed services offered by local houses of worship and nonprofit groups. Many people come in off the streets in search of help with their rent or other household expenses, Moore said.

Her church, which operates a soup kitchen on its vast property, has become a prime destination for families seeking warmth during the winter. The demand led First Christian to spend $2,500 to upgrade its fire alarm system.

Moore said county leaders have shown “a lack of courage and moral initiative” when it comes to finding ways to create more affordable living options.

Mark Zetts, who chairs the planning and zoning committee for the politically influential McLean Citizens Association, said homeowner groups support creating more affordable housing but had reservations about the proposed Residential Studio Unit ordinance.

The legislation — which was the subject of 24 public meetings and two workshops — was too broad of an approach to what can be a complex problem, Zetts said.

For one, many lower-income people in need of cheaper homes also require a network of social services, which the ordinance didn’t provide for, he said.

Another problem was that the ordinance allowed as many as three people to live in a new studio but required developers to provide only one parking spot per unit, Zetts said.

“They promoted this as housing stock, but that ignores some of the problems that go with it,” he said. “One size does not fit all here.”

Gomez said she longs for a home to call her own.

A housekeeper who arrived from Peru in 1998, she lost some of her customers as the economy tightened. About four months ago, she found she could no longer afford the apartment where she and her sons lived alone.

She found out about the apartment near Falls Church through an ad in a neighborhood laundromat. It offered a room with living space and shared use of a kitchen for $700 a month, she said.

On a recent day, Gomez stood in her apartment and spoke in hushed tones about the friction with her apartment mates that stems from living in such tight quarters. In the modest, two-bedroom residence, every dirty dish or a stray toy can loom large.

“They call everything to my attention,” Gomez said, while her son Henry, 13, played in the living room with a pair of not-so-young chicks given to him by a family friend.

Her other son, Danery, 7, is a burst of energy eager to engage anyone in talk about soccer or whatever else is on his mind. He shows affection for his older brother by bouncing all over him — behavior, Gomez said, that has triggered objections from her apartment mates.

“They complain that [the boys] break things, that they don’t clean up,” she said. “We had a bicycle, but we had to get rid of it. Where am I going to put it?”

One of her apartment mates lamented the lack of space as well. “Where does one go to find a comfortable place that is affordable?” said Alberto Cox, a house painter who is also from Peru. “I have no idea.”

On a recent hot summer afternoon, Danery practiced kicking his soccer ball in the living room while Henry sat in front of the TV.

When Cox arrived home from work, the boys went into their bedroom. Cox was soon out the door again, on his way for a jog.

“It’s good for the nerves,” Cox said, smiling, as he made his way through a narrow living room path toward the front door.