The education measure requires states to distribute the money for the current school year, but allows school districts to spend it as late as September 2012. It also allows schools to roll back furlough days. The education department estimates it could salvage about 160,000 jobs.

“We can’t stand by and do nothing while pink slips are given to the men and women who educate our children or keep our communities safe,” President Obama said last week. “That doesn’t make sense.”

Though preserving jobs will be good for the economy, it will disappoint out-of-work teachers and parents who have been expecting a surge in rehiring. Many districts, like Kansas City, Kan., face the likelihood of midyear cuts, and administrators will count themselves lucky to save jobs. In the nation’s fifth-largest district in Clark County in Las Vegas, administrators are eager to hire some teachers, though they wonder what they will do when the federal money runs out.

“We’re a little wary about hiring people if we only have money for a year, but we know that’s the intent of this bill,” said Jeff Weiler, chief financial officer for Clark County schools.

In Texas, Republican Gov. Rick Perry so far has rejected the new federal education dollars. Should he relent, Houston’s superintendent, Terry B. Grier, proposes to use $40 million to $70 million of it to extend the school day and year, and to hire tutors. He does not plan to rehire 414 people  including quite a few certified teachers  laid off from the central office staff.

Image A 2009 job fair for teachers. The stimulus bill was intended to rehire 160,000 workers. Credit... Charlie Riedel/Associated Press

“We can’t treat this money as if it’s a supplement to a jobs bill,” Mr. Grier said. “I want to put people to work to help children.”