In the five years since they began their life together in the desert sprawl of greater Phoenix, Devon Lawrence and Eren Mendoza have bounced from one itinerant home to another.

They have camped alongside a freeway off-ramp, using a gas station sink as their bath and a plastic tarp as their refuge from the relentless sun. They have slept on an air mattress in a friend’s living room. For the last two years, they have crammed into rooms at motels, paying as much as $650 a week.

Ms. Mendoza and Mr. Lawrence are both 32, and both have jobs. She works at a supermarket deli counter. He stocks shelves at a convenience store. Together, they earn about $3,500 a month. Yet they have been stymied in their reach for a modest dream: They cannot find an affordable home in a safe neighborhood in Phoenix, where rents have roughly doubled over the last decade.

“These prices are just wild,” Ms. Mendoza said. “It’s pretty much all anybody talks about. The fact that a dual income can’t support us is insanity.”

The impossible arithmetic of housing is a potent source of economic anxiety in Phoenix, and in many major American cities — a reality that could influence control of the White House.

Arizona is one of six battleground states likely to determine the result of the presidential election. Its unemployment rate was only 3.7 percent in February, lower than the 3.9 percent national rate. Inflation has slowed. In the Phoenix area, optimism is buoyed by $60 billion in investments in factories that make advanced computer chips — a Biden administration talking point.

But polls consistently reveal economic pessimism, threatening President Biden’s tenure. More than half of Arizona voters rated economic conditions as “poor,” and another one-fourth as “fair,” in a New York Times/Siena College poll of battleground states last year.

National polling in February found improving assessments about the economy, yet worsening evaluations of Mr. Biden’s performance. More than 90 percent of respondents who rated the economy poor or fair had a negative view of the housing market. Mr. Biden has recently outlined proposals to lower the costs of home-buying while spurring the construction of affordable options.

Arizona exemplifies the stress over housing. Over the past decade, the allure of suburban life under cloudless skies has swelled the population of greater Phoenix to five million from 4.2 million, according to census data. The influx pushed housing prices steadily higher.

At the same time, restrictions on development, public opposition to growth and severe disruptions to the supply chain for building materials limited the construction of new housing. This is especially so for lower-income households because their profit margins are limited and they depend on subsidies.

Since 2010, the number of rental properties available for $1,000 or less in greater Phoenix has declined 86 percent, according to the Maricopa Association of Governments, a regional planning agency. The number of homes selling for $300,000 or less dropped 73 percent.

Those sorts of properties “used to be the majority of our market,” said Amy St. Peter, the agency’s deputy executive director. “They are virtually nonexistent now.”

For lower-income households, the mass disappearance of affordable housing has produced a wave of evictions, a surge of homelessness and desperation.

Even for people of greater means, an atmosphere of crisis grips housing. As the price they must pay to become homeowners soars, young professionals with six-figure incomes are taking on extra jobs and longer commutes.

Real estate agents — a professionally optimistic lot — cannot shake a gnawing sense of futility.

“Most people making $45,000 to $90,000 a year can’t afford to buy a house, and that makes people feel like the economy is crummy,” said Nathan Claiborn, an agent at Carin Nguyen Real Estate in the Phoenix area. “Housing affordability is a psychological drain for everyone.”

What the bubble built.

The story of how Phoenix became a wildly expensive place to live stems directly from how it previously beckoned as a bastion of affordability.

In a nation reared on the mythology of the inexhaustible frontier, Arizona’s cactus-dotted landscape stretched to horizons that seemed limitless. Developers exploited the availability of land to sell the dream of Spanish-tiled roofs and swimming pools at discount prices — an antidote to the severe housing problems afflicting neighboring California.

Phoenix became the center of the speculative real estate boom that filled out the first years of the new millennium. The reckoning that followed yielded a wave of foreclosures. Local communities imposed restrictions on development.

Still, the population grew, especially during the pandemic, as professionals working from home sought larger properties in distant suburbs. From 2021 to 2022, Maricopa County — which contains much of greater Phoenix — added 57,000 people, registering the largest population growth in the nation.

As the Federal Reserve lifted interest rates to lower inflation, mortgage rates increased sharply, raising the costs of buying homes. Homeowners who might have sold properties — empty-nesters seeking smaller homes, and young parents needing extra bedrooms — have stayed put. That has limited the supply of homes on the market, keeping prices high.

Measures of affordability generally assume that a household should spend no more than 28 percent of its gross income on housing. By that criteria, only about one-fifth of all homes sold in the Phoenix area late last year were affordable for a family earning the median local income, about $72,000, according to an index maintained by the National Association of Homebuilders and Wells Fargo. Before the pandemic, nearly two-thirds of local homes were priced at affordable levels.

Housing experts generally concur on the solution: Increase the density of neighborhoods, adding apartments at rates subsidized by tax credits. But most of the available land in Phoenix and its surrounding suburbs is zoned for single-family homes.

Community activists have used social media to sow alarm about the prospect of affordable housing projects. They have warned of rising crime and diminished property values in pressing an age-old mantra: Not in My Backyard.

“The vocal minority in many communities are creating this avalanche of NIMBY-ism,” said Debra Z. Sydenham, executive director of the Urban Land Institute Arizona District Council, a nonprofit group. “We are talking about providing homes for firefighters, for teachers, for nurses, for police officers. They view it as, ‘No, you’re providing homes for drug addicts.’”

Which helps explain why people like Eren Mendoza and Devon Lawrence remain stuck. Even if they could find an affordable apartment, they could not pass a credit check, given his student loan debt. They cannot come up with the first and last month’s rent plus the security deposit.

This also explains why Constable Lennie McCloskey is an especially busy man.

‘You have to leave.’

Constable McCloskey — known to his fellow municipal officials as “Lock ’em out Lennie” — spends much of his time evicting tenants who have fallen behind on their rent.

“They know they’ve got to leave,” he said. “I explain to them: ‘It’s only a contract. You agreed to do something. You didn’t do it. You have to leave.’”

Last year, landlords filed 83,000 evictions in the Phoenix metro area, the highest total since 2005, according to the Maricopa Association of Governments. The increase in part reflected the ending of a pandemic-era moratorium on evictions.

On a recent morning, Constable McCloskey, 68, scanned the paperwork on a dozen fresh cases on his beat in the Western Valley. He donned a black bulletproof vest with a Maricopa County badge, and a holster bearing a green-handled 9-millimeter pistol.

He conducted his rounds with jovial aplomb, counseling people not to lose hope even as they scrambled to pack belongings in the minutes he allotted before ordering them out.

“Typically, it’s five to 10 minutes,” he said. “If they’ve got kids and pets, I work a little bit of time with them, but usually I won’t go more than 30 minutes.”

In the bedroom community of Peoria, Mr. McCloskey rousted a half-dozen squatters from a dilapidated home littered with drug paraphernalia, unwashed dishes and a mostly eaten birthday sheet cake.

He drove to an apartment complex in Glendale, near the Arizona Cardinals football stadium, to remove Leebert George Brown, 35.

Mr. Brown’s place was spotless, its white countertops glistening. He had lived there since August, when he moved to Phoenix from his native Florida, in pursuit of work as a plumber. The rent, nearly $1,600 for a one-bedroom apartment, seemed manageable once he cracked the ranks of the plumbers’ union.

But his application had been held up. He was driving for Uber and working nights at an Amazon warehouse, where he earned $17.63 an hour. He was falling behind, while sending money home to his mother, who suffered seizures.

He had packed most of his belongings by the time the constable arrived — his clothes, his high school diploma, some personal finance books. As a maintenance man changed the locks, he grabbed his work boots. He would need them for his shift at Amazon in less than five hours. He would get off work at 5 the next morning. Then where would he go?

Mr. Brown shrugged. “I’ve got to work something out,” he said.

The constable held the door for him as he stepped into the hallway and headed toward the elevator, carrying his clothes in two plastic trash bags.

“Sorry it took me so long,” Mr. Brown said.

“Thank you for your cooperation,” the constable replied.

‘It doesn’t work.’

In downtown Phoenix, at a homeless campus run by a nonprofit group called Keys to Change, the staff has grown accustomed to people arriving with problems like addiction and domestic violence. Those unable to pay market rents have run out of couches to crash on. They have exhausted assistance from sympathetic friends and relatives.

Even wealthy people are confronting compromises that have undermined their faith in the economic system.

Alexandra McDaniel, 29, grew up in Scottsdale, the affluent suburb north of Phoenix. As she and her fiancé, Cameron Smith, 32, began their search for a home early this year, she hoped to live close to her parents, and near her job at a fashion retailer. Mr. Smith was intent on finding an area where Ms. McDaniel could safely walk their dog alone at night.

Mr. Smith is a data analyst at Amazon. Together, he and Ms. McDaniel earn roughly $200,000 a year. They figured they could afford to pay as much as $550,000 for a home, though they aimed lower.

But as they sat in a conference room on a recent morning, their Realtor, Curt Johnson, projected a map on a screen that forced them to downgrade their expectations.

He had searched for houses with small pools and at least three bedrooms priced at $475,000 to $575,000. Scottsdale had no listings. The half-dozen properties he had found were scattered about 15 miles away, and beyond a freeway.

“It’s a lower-income area,” Mr. Johnson said, adding that it had “a higher crime rate.”

He drove the couple out for a look. The first two homes had tiny yards unsuitable for their dog. The third place had a huge yard and a wide-open kitchen, but the asking price was $599,000. The next one was similarly priced, and the neighborhood felt seedy. The last house was within their budget, but alongside an apartment complex whose balconies looked directly into the yard.

As they drove back to Scottsdale, they struggled to make sense of their situation.

“We have great jobs,” Ms. McDaniel said. “We’re doing exactly what we were told to do, and it doesn’t work.”