(Credit: Olivier Douliery-Pool/Getty Images)

At the White House today, Education Secretary Arne Duncan sounded the alarm over looming automatic cuts to the nation's school system, warning that as many as 40,000 teachers could lose their jobs with some layoffs already underway.

It's an eye-opening claim, but one not entirely supported by facts.

"Over the next, you know, month or two, you'll see lots of pink slips go out," Duncan said. "That's starting," he added, "it's still really early on."

The secretary told reporters today that in "a couple districts," including Kanawha County, W.Va., Title I and Head Start teachers have already received the bad news that they will be out of work. It's a claim he first made publicly Sunday on CBS' "Face the Nation."

"There are literally teachers now who are getting pink slips, who are getting notices that they can't come back this fall," he said at the time.

Experts agree that widespread teacher layoffs could eventually become reality if the package of deep spending cuts known as sequester is allowed to hold. But they say there is little sign a wave of pink slips has begun.

Kanawha County officials told ABC News that no pink slips have been issued this year because of budgetary issues or the sequester, and that no contingency plans have been drawn up in case the automatic cuts do take hold.

"We're just waiting to hear whether these cuts go through and how much money we'll lose," said one administrator, who asked not to be identified.

Pam Padon, director of federal programs and Title 1 for Kanawha County public schools, told the Washington Post that "transfer notices" were sent to 104 teachers, informing them that they may have a new assignment starting next fall, and that some of those transfers could ultimately mean several people lose their jobs.

County officials, speaking on condition of anonymity to ABC News, confirmed the report, but said that those notices were not considered layoffs or pink slips and have nothing to do with sequestration.

The American Association of School Administrators has offered a similar assessment of the current state of play, saying it knows of no sequester-related layoffs among its members. The full scope of necessary layoffs won't be known until local districts assess the budgetary damage from sequester, if it takes effect, and develop plans for the coming school year, officials have said.

A spokesman for the Education Department did not respond to ABC News' request for comment on the secretary's claims. Duncan did qualify his active-layoffs claim with this: "Whether it's all sequester-related, I don't know. But there are teachers who are getting pink slips now."