By CHARLES FORELLE

LISBON—Isabel Fernandes, a cheery 22-year-old with a constellation of stars tattooed around her right eye, isn’t sure how many times she repeated fifth grade. Two, she says with a laugh. Or maybe three. She redid seventh grade as well. She quit school with an eighth-grade education at age 20.

Ms. Fernandes lives in a poor suburb near the airport. She doesn’t work. Employers, she says, “are asking for higher education.” Even cleaning jobs are hard to find.

Portugal is the poorest country in Western Europe. It is also the least educated, and that has emerged as a painful liability in its gathering economic crisis.

Wednesday night, the economic crisis became a political crisis. Portugal’s parliament rejected Prime Minister José Sócrates’s plan for spending cuts and tax increases. Mr. Sócrates handed in his resignation. He will hang on as a caretaker until a new government is formed.

Without the budget cuts, Portugal is almost certain to need an international bailout. It will run out of money this year without fresh cash, and markets are charging punitive rates for borrowing. Two firms downgraded Portugal’s credit rating Thursday.

Its dire situation thrust a possible Portuguese rescue onto the agenda of European Union leaders who gathered in Brussels Thursday for a previously scheduled meeting, where they were agreeing on a new bailout fund. Portugal would be the third country in the euro zone to require a bailout, after Greece and Ireland.

The state of Portuguese education says a lot about why a rescue is likely to be needed, and why one would be costly and difficult. Put simply, Portugal must generate enough long-term economic growth to pay off its large debts. An unskilled work force makes that hard.

Cheap rote labor that once sustained Portugal’s textile industry has vanished to Asia. The former Eastern Bloc countries that joined the European Union en masse in 2004 offer lower wages and workers with more schooling. They have sucked skilled jobs away.

Just 28% of the Portuguese population between 25 and 64 has completed high school. The figure is 85% in Germany, 91% in the Czech Republic and 89% in the U.S.

“I don’t see how it is going to grow without educating its work force,” says Pedro Carneiro, an economist at University College London who left Portugal to do his postgraduate studies in the U.S.

The education woes in Portugal show the extent of Europe’s challenge as it tries to right itself amid the sovereign-debt crisis.

Rapid and painful budget-cutting, which is being enforced across the Continent, is the first step. But the second is far harder and will take far longer. The 17 countries linked via the euro have vastly differing levels of economic performance. Unless the gulf is narrowed, the pressures that caused the weaker among them to pile up huge volumes of debt, and have trouble repaying it, will doubtless re-emerge.

Better schooling in Portugal won’t come quickly. Sharp cuts in its education spending make the task harder. And even if there are improvements, reaping their benefits could take years.

Greece and Ireland, the two EU countries that got bailouts, reached the brink relatively rapidly: Greece came undone after revelations it had grossly underestimated the government’s parlous fiscal state; Ireland self-immolated in an orgy of property speculation.

Portugal’s crisis, by contrast, has come to a boil slowly. For a decade, Portugal’s growth trailed the euro-zone average. Traditional industries like cork harvesting and shoe stitching couldn’t energize the entire country. The tech boom of the mid-2000s largely passed Portugal by.

The Portuguese spent nonetheless. The economy—government and private sector together—has run cumulative deficits with the rest of the world of more than €130 billion over the past decade. The state hasn’t had a balanced budget, let alone a surplus, for more than 30 years.

The result is a pile of debt. The government’s debt, some of which is held domestically, will approach 90% of gross domestic product this year. The entire economy, including both the public and private sectors, owes foreigners an amount equal to more than two years’ of economic output.

Before his failure this week, Prime Minister Sócrates had pushed some budget cuts through parliament under pressure from other euro-zone countries. But in an interview before Wednesday’s political crisis, Mr. Sócrates made clear that investment in education was a priority, despite the costs. Appeasing financial markets was important, he said, but the country shouldn’t “lose the strategy and vision.”

There is substantial evidence from elsewhere that education confers broad economic benefits. Ireland was one of the EU’s poorest countries a generation ago. But it threw EU subsidy money into technical education and remade itself as a destination for high-tech labor, made doubly attractive by low corporate taxes. Ireland is now, even after a brutal banking crisis, among the richest nations in Europe.

“They had an educated-enough work force that they could move into a technology industry, and they rose out of nowhere,” says Eric Hanushek, a Stanford University professor.

Prof. Hanushek and a professor from the University of Munich have linked GDP growth with population-wide performance on standardized tests. They calculate that Portugal’s long-term rate of economic growth would be 1.5 percentage points higher if the country had the same test scores as super-educated Finland.

Education long was an afterthought here. “The southern countries like Portugal and Spain and the south of France and Italy, we have always had some problems related with education,” says António Nóvoa, a historian who is rector of the University of Lisbon. “That’s been like that since the 16th century.”

The repressive dictatorship that ruled Portugal from 1926 to 1974 had the idea “that people should not have ambition to be something different than what they were,” Mr. Nóvoa says. The result was widespread illiteracy and little formal schooling; just three years were compulsory. Huge leaps have been made since the 1970s, he says, but “it is not easy to change a history of five centuries.”

Portugal has just begun phasing in 12 years of required schooling; now, Portuguese can leave school after ninth grade. Many do. The government says it is racing ahead with reforms. Mr. Sócrates points to an initiative that gives students laptops and to a far-reaching project to rebuild dilapidated schoolhouses. Results last year show students improving on standardized tests.

But it is a long road. “We have accumulated years and years of ignorant people,” says Belmiro de Azevedo, a billionaire industrialist.

He described the system as calcified. The central administration wields tight control. Curricula are simultaneously undemanding and rigid. Dropout rates are high. Schools struggle to accommodate an influx of immigrants from Portugal’s former colonies in Africa, such as Angola and Guinea-Bissau.

A push to evaluate teachers triggered searing strikes and demonstrations in 2008, souring relations between powerful teachers’ unions and the government. The political life of education ministers is measured in months: since the dictatorship ended in 1974, there have been 27.

To the system’s critics, a fight that has developed over quasi-private schools is emblematic of what’s wrong. With budgets tight, the government has imposed deep cuts on schools that are at the margin of the state’s control—no matter that some are among the best.

The highway north of Lisbon rises gently out of the Tagus River’s estuary and cuts through valleys of pine and scrub and fields stained yellow by sweet clover. About 30 miles up, in the municipality of Torres Vedras, the population is spread thinly in tiny towns that dot roads meandering toward the ocean.

In one town, A Dos Cunhados, the local school isn’t run or owned by the government. It is managed by the Catholic Church, in an arrangement that dates to the end of the dictatorship, when the new Portuguese state found it didn’t have enough facilities.

At the school, Externato de Penafirme, as at 90 others with what are called “association contracts,” the state pays a management fee to a private entity, which broadly follows the state curriculum but hires its own teachers.

The deputy principal, Carlos Silva, once taught chemistry in the public school system. He was shuffled through four schools in four years. Frustrated, he quit and enrolled in a seminary. Afterward, as a priest, he asked his bishop about returning to the classroom, and was assigned to Externato de Penafirme.

Instead of being given teachers off a master list, Father Silva and other administrators of these quasi-private schools select their own. They adjust the curriculum, adding, for instance, more religious instruction. They set up teams of teachers responsible for students and try to rope back those prone to dropping out.

“We make an enormous effort to take them all to the end,” says a school administrator, José Mendes. Penafirme’s test scores put it in the top 15% of secondary schools nationwide. It is the best in Torres Vedras.

To their advocates, the privately run schools inject a needed dose of new thinking. “We have to keep a diversified system,” says Eduardo Marçal Grilo, a former education minister. If there’s a public and a private school in the same place, he says, “let’s see what is the best, and if the best is private, the state can close the public and support the private.”

But in November, the priests of Penafirme got a shock. Facing money problems—the government’s education budget is declining 11% this year—the education ministry said it would cut the sum it pays association-contract schools to €80,000 per class, from €114,000 on average. Father Silva says it spends €85,000 per class on salary and benefits alone.

To the current education minister, Isabel Alçada, directing scarce funds to private entities like Penafirme while regular public schools have grave needs “is not just.” What was once a program meant to fill gaps has turned into “competition,” she complains, in which private operators set up bus routes to lure students.

Faced with the cuts, students and parents organized. In December, 4,000 people held hands in a big ring around the Penafirme campus. The pictures hit television. A Facebook group sprang up. In January, students walked out of dozens of the privately run schools for three days. To dramatize a claim the cuts would mean the death of their schools, students and parents from 55 schools ferried mock coffins to Lisbon and put them on the median strip outside Ms. Alçada’s ministry.

Last month, the education ministry eased somewhat, agreeing to restore part of the lost funding for this semester.

Paulo Gonçalves, a Hewlett-Packard Co. corporate salesman who is president of the Penafirme parents’ association, says the détente was a victory, but more money is needed to keep quality high enough to prepare students for college. “If you earn a degree in Portugal, you earn more or less double those who don’t,” he says. “This is what I teach my kids.”

It’s particularly true with unemployment over 11%. “With the crisis, we have to go to university,” says Sophie Alves, a Penafirme senior who plans to study occupational therapy in college. With only a high-school diploma, “you can do nothing, just serve tables.”

With even less than that, prospects are bleaker still. Ms. Fernandes, the 22-year-old with an eighth-grade education, comes often to a school in Apelacão, where a tiny nonprofit called Project Leadership tries to coax young people back to class or help them get jobs.

Serafim Gomes, also 22, was there on a recent afternoon. He left school in eighth grade with the dream of becoming a professional soccer player. It didn’t pan out. Now he occasionally waits tables and hopes for better employment.

Marco Monteiro, who is 16, was recently kicked out of his regular school. Bad behavior, he says. He hoped to go back—”I don’t have enough school to find work,” he says—and then maybe get a job in the mall. Project Leadership’s director, António Embaló, complimented him on his mechanical skills.

Might he consider college, perhaps studying engineering?

“It’s never crossed my mind,” Mr. Monteiro says. “I don’t know anyone who went.”