Some might call it blackmail. The governor of Wyoming calls it desperation.

Governor Dave Freudenthal is threatening to sell off a chunk of one of America's most beautiful national parks unless the Obama administration comes up with more money to pay for education in the financially beleaguered state.

He says he will auction land valued at $125m (£80m) in the Grand Teton national park, one of the country's most stunning wildernesses. Part of the park was donated by John Rockefeller Jr.

Other parts belong to the state government including two parcels of land of about 550 hectares (1,360 acres) designated as school trust lands to be "managed for maximum profit" to generate funds for education in Wyoming.

At present Wyoming raises only about $3,000 a year from the land by leasing it to a cattle rancher. Officials have menacingly suggested that the property might make a nice site for a ski lodge.

Freudenthal recently wrote to the interior department asking the federal government to trade the park land for mineral royalties. "If the federal government won't dance with us, we will go look for another partner," said Freudenthal. "The purpose is to force the federal government to come to the table."

Washington says it is negotiating, but Freudenthal says the issue has dragged on for a decade. "The way the federal government has treated us to date is that we are like the people who own the land, but they figure there isn't anything else they can do with it," he said.

Previous negotiations led Washington to offer 800,000 acres of federal land in a swap but state officials rejected it as "trash land" not worth nearly as much as their "prime, in-park real estate".

"I admit we aren't as bright as those boys on the Potomac," said Freudenthal. "But this ain't our first county fair."

• This article was amended on 11 August 2010. The original headline was US National Park faces sale. This has been corrected.