PORTLAND — Leafy, progressive and prosperous, it sometimes seems as though Oregon’s largest city can’t go a month without being singled out for national plaudits, be it Fit Pregnancy’s pronouncement that the city is tops for breast-feeding or Prevention magazine’s crowning of Portland as the country’s best urban area in which to go for a walk.

But beyond the praise for a city often celebrated — and emulated — for its urban quality-of-life is a public school system that’s undergoing a very public identity crisis, slumping under years of state budget cuts and declining enrollment.

A proposal recently leaked to the news media outlined a plan to close 11 of the city’s elementary schools, and transform more than two dozen of the rest into combination elementary-middle schools, a sweeping change that could ultimately touch thousands of children in the district.

Even people who could afford to send their kids to private or parochial schools in Portland have a long history of supporting the city’s public school system. Nearly 90 percent of students living in the city go to public school, compared to just 80 percent in nearby Seattle, and 77 percent down the coast in San Francisco, according to Census Bureau data.

But some say this latest proposal could spark a parental exodus, leaving a sizable dent in Portland’s carefully burnished national reputation for livability in its wake.

“Neighborhood schools are keeping families in Portland,” said Ruth Adkins, a parent activist whose daughter Harriet attends a small, tidy elementary school slated for closure. “My husband can walk our daughter to school, then take the bus downtown. We can walk to the park, the pool, the library, and that’s repeated all over town. I just hope people don’t vote with their feet.”

In cities like New Orleans or Detroit, where middle and upper class families have largely forsaken city school systems for the suburbs, private schools or home-schooling, the fallout quickly spilled over into the community-at-large, experts say.

“The middle class has the wherewithal to spend the time and money that we need to support the schools in a way that some other populations might not be able to do,” said Sheila Martin, who directs the Institute of Portland Metropolitan Studies, at Portland State University. “Parents are the ones who volunteer to help with extra-curricular activities, with reading and art, with fund-raising.”

Portland’s current problems have two roots. The first is a pending $57 million hole in the schools budget, already down after state budget cuts and worsened because a three-year temporary income tax for schools support runs out this year, as does a property tax levy and federal desegregation money.

And even Portland’s famously liberal voters — who haven’t forgotten that years ago, George Bush Sr. dubbed the city “Little Beirut” — showed no inclination to vote for more schools taxes.

City, county and state leaders are frantically scavenging for one-time money to shore up the district for the next year, on the theory that as go economic-engine-Portland’s fortunes, so follow the rest of the state. And a one-time windfall from the state school fund and a district health fund could add about $9 million more to the district’s bottom line, if board members decide to use the money right away.

But even an infusion of such Band-Aid funds would still leave the district needing to make at least $15 million in cuts, from a total budget of almost $400 million.

There’s also the enrollment issue. In the 1970s, enrollment in the city’s public schools peaked at more than 80,000 students. Since then, though, close-to-downtown neighborhoods have gentrified rapidly, housing prices have zoomed and suburban schools ringing the city have boomed.

That’s driven down the number of students left in Portland public schools to around 47,000, one reason schools Superintendent Vicki Phillips said the district needs to get serious about closing buildings, and pooling its remaining resources to ensure that every school can offer a core curriculum, plus tempting electives like art, music and gym.

“I didn’t come here to do harm to Portland — even after my job, I want to live here, and this is the first place I can say that,” said Phillips, the former Pennsylvania state schools superintendent, who has also worked in Kentucky and Washington, D.C. “We just need to make the most of our reality.”

Phillips said district officials could have just redrawn boundaries, but wanted to preserve Portland’s tradition of neighborhood schools. So she’s pushing instead for combined elementary-middle schools, to be located within existing boundaries. The change is big and sudden, she admits, but says that the end result would mean more long-term stability than the system has seen in years.

Parents say they feel an ethical, emotional pull toward supporting the public schools, but worry about the near-constant upheaval and its fallout on their sons and daughters. Hundreds of parents have been turning out for school budget forums across the city in recent weeks, urging school board members to slow down the timeline for school closures and restructuring.

“The flux our kids are in all the time, it’s not fair for them,” said Christine Schutzer, who has one child in the system, and another set to enter kindergarten next year. “Of course, we feel like the public schools have to work. If everyone who can flee, does, the city is in big trouble. But my children do have to come first.”