Schools across the country are sending out pink slips as they brace for the possibility of deep federal budget cuts that could take effect next week, Education Secretary Arne Duncan said Thursday.

Duncan criticized Congress for failing to reach a deal to stop the across-the-board cuts, known as sequestration, which could force thousands of teachers out of their jobs.

“There’s no one in their right mind who would say that this is good for kids or good for the country, yet somehow it becomes tenable in Washington,” Duncan said. He said that “there is no fix” to mitigate the impact of the cuts.

Federal officials estimate that they will be forced to trim more than $1.3 billion in education spending, most of which goes toward programs for poor children and students with disabilities.

Most schools would not face the full effect of those cuts until the fall. But schools that receive more federal aid — including Department of Defense-run schools and those on Indian reservations — are likely to feel the squeeze immediately, which could mean shorter school weeks in spring or a shorter school year.

“These are two populations that we owe more to, not less,” Duncan told a group of reporters in Washington, “and those cuts are going to kick in quicker.”

In addition to potential cuts, Duncan addressed a wide range of subjects related to the Obama administration’s second-term education goals.

Those goals include expanding access to public preschool, encouraging high schools to offer more career and technical education and — two months after a shooter gunned down 26 students and teachers at Sandy Hook Elementary School in Newtown, Conn. — ensuring that schools are safe.

Security doesn’t mean asking teachers to carry weapons into classrooms, Duncan said, calling that idea — floated by the National Rifle Association after the Sandy Hook massacre — a “marketing opportunity.”

“The vast majority of teachers have spoken pretty loudly and said they’re not interested in being armed. That’s a red herring,” Duncan said. “It’s just an opportunity to sell more guns. That’s a marketing opportunity. That’s not serious.”

The Obama administration is pushing legislation that calls for universal background checks for gun sales and a renewed ban on assault weapons.

Duncan said stemming violence requires not just tighter gun controls but a broad effort to improve opportunities for young children.

One part of that effort will be to expand public preschool, he said. “If we can have a generation of children enter kindergarten ready to be successful and close that opportunity gap, that’s a life-transforming thing for those kids and their family.”

Duncan has exercised unusual influence over education policy during the past four years, using carrots — such as billions of dollars in stimulus funding — to encourage states and school districts to adopt reforms the Obama administration favors.

He also has offered nearly three dozen states relief from the most onerous provisions of the No Child Left Behind Act, the George W. Bush-era federal education law that was supposed to be rewritten six years ago but has stalled in Congress.

To get a waiver from No Child Left Behind, states had to outline alternative accountability plans that Duncan deemed acceptable. Republican critics say the waivers have given the federal government too much power over state policy, and they have hinted that rewriting the law would be an opportunity to rein in that role.

Duncan said he “desperately” wants to pass a new version of the law but refrained from offering a timeline. “We need to get that done at some point,” he said.