Tens of millions of Brazilians have risen out of poverty over the past decade in one of the world’s great economic success stories. The reasons are many: strong overall economic growth, fueled by exports. A rise in the minimum wage. A more educated workforce. And big government spending programs, including direct payments to extremely poor families.

But becoming middle class in Brazil means a better life, not an easy one. The new, lowest rung of the middle class is what in the U.S. would be called the working poor, with monthly incomes of between $500 and $2,000.

Yet this group is driving consumer spending in Brazil as they cobble together enough money to buy a television, a cell phone or pay for their children to go to a private school.

In the northeastern city of Recife, I stopped in at the Walt Disney School. It has a crenellated roof that…