“And they’re asking for another 11 percent increase next year and the next, and that’s where I’m saying I just don’t know how,” Fawzia Keval, the school’s principal, said. “I’m spending sleepless nights.”

Across the nation, far more schools failed to meet the federal law’s testing targets than in any previous year, according to new state-by-state data. And in California and some other states, the problem traces in part to the fact that officials chose to require only minimal gains in the first years after the law passed and then very rapid annual gains later. One researcher likens it to the balloon payments that can sink homebuyers.

Part of the reason for the troubles was that the states gambled the law would have been softened when it came up for reauthorization in 2007, but efforts to change it stalled. This year Congress made no organized attempt to reconsider the law. With the nation facing urgent challenges, including two wars and economic turmoil, it could be a year or more before the new president can work with Congress to rewrite the law.

The law requires every American school to bring all students to proficiency in reading and math by 2014. When it was first implemented six years ago, it required states to outline the statistical path they would follow on their way to 100 percent proficiency, and about half set low rates of achievement growth for the first few years and steeper rates thereafter.

Here in California, which in 2002 had only 13.6 percent of students proficient in reading, officials promised to raise that percentage on average by 2.2 points annually from 2002 to 2007, but starting this year greatly accelerate the progress, raising the percentage of proficient students by 11 points per year through 2014.