The nation's largest synthetic fuels project, which has survived one financial cliffhanger after another, may finally run out of luck in the next few weeks.

The fate of the Great Plains project in North Dakota was thrown into doubt when officials of the Synthetic Fuels Corp. made clear that they would not approve the $820 million in federal price supports demanded by the project's sponsors.

The sponsoring companies, led by Tenneco and American Natural Resources, have received $1.5 billion in federal loan guarantees. But they said two weeks ago that they are likely to close the coal-gasification plant by June 15 unless the additional price guarantees are approved.

The decision to reject the year-old request for further aid may signal a tougher approach by the federally funded corporation. But the demise of the industry's showcase project also could help efforts by leading House Democrats to abolish the synfuels program.

Thomas J. Corcoran, the corporation's new vice chairman, said the Great Plains sponsors should "not be permitted to take $820 million in federal price supports and then abandon the project in two or three years." He said a new analysis by the Reagan administration found that the sponsors are likely to close the plant by 1988 after they have exhausted many of its tax benefits.

If the plant is shut down now instead of later, Corcoran said, "then we wouldn't have wasted $820 million from the Synthetic Fuels Corp."

Joel Melarvie, vice president of Great Plains Gasification Associates, acknowledged that the plant may be closed within three years, even with the new federal aid, if energy prices remain flat and the sponsors keep losing money. But if the price guarantees are withheld, he said, there is "a very, very strong possibility" that the plant will be closed by June 15.

"We've always been faced with possibility of abandonment, almost from day one," Melarvie said. "It's been one thing or another leading us to the brink. This latest action is no exception . . . . But we are still hopeful that something can be worked out."

The plant near Beulah, N.D., which employs 950 people, is producing the equivalent of 12,000 barrels of oil a day.

Corcoran recently told a House Government Operations subcommittee that there is no way the five-member synfuels board will provide the four votes required to release the $820 million in aid its staff recommended. Corcoran is a former GOP congressman from Illinois who had been one of the sharpest critics of the synfuels program.

Subcommittee Chairman Mike Synar (D-Okla.), who wants to do away with the synfuels program, called Great Plains "a financial nightmare. It is simply not economic under anyone's expectations. The bottom line is that the sponsors cannot operate Great Plains and service their debt to the taxpayers of $1.46 billion."

Critics say the Great Plains saga is typical of a program that has funded only two major projects in its five-year history and has offered to buy experimental fuels for a price of up to the equivalent of $92 for a barrel of oil. This meager track record has been caused in part by a worldwide oil glut that has depressed energy prices and driven oil companies out of the fledgling industry.

Supporters such as House Majority Leader James C. Wright Jr. (D-Tex.) acknowledge that the program has been plagued by mismanagement, but they say developing alternative energy sources is vital to national security. Congress cut synfuels funding by $5 billion last year, leaving the corporation with $8 billion it has yet to hand out.

The Great Plains project was launched with a $2 billion line of credit backed by the Energy Department. But the sponsors threatened to abandon the project in 1983 unless they received more than $1 billion in price guarantees.

The Synthetic Fuels Corp. tentatively approved the request under pressure from the White House and congressional leaders. But the board lacked a quorum for months, then got two new members who have been unable to vote on the scaled-down aid request because of possible conflicts of interests.

One member, Paul W. MacAvoy, sits on the board of a company whose subsidiary has been the contract manager for Great Plains. The wife of the other, Eric H. Reichl, owns about $76,000 in stock in two of the sponsoring companies.

The next setback came when the General Accounting Office reported that the sponsors could earn a 19 percent rate of return on the project, even without the $820 million in price supports. But the sponsors said it would take them until the 1990s to see those profits.

Corcoran said the administration's analysis found that the plant's tax benefits outweigh the investment by the five sponsors, who would have to pay a $360 million penalty if they bailed out today. By 1988, he said, the tax benefits and the penalty will dwindle and the loans will come due -- all incentives for an early shutdown.

Energy Secretary John S. Herrington recently said he will oppose the price guarantees unless Great Plains agrees to stretch out repayment of the loans his department backed, a move designed to ensure that the plant stays in business.

Melarvie said the sponsors are weighing the demand, but added: "A new factor has been introduced after 17 months of negotiation. It's not fair to bring this up at this late stage of the game."

Corcoran said it is possible that a funding compromise may be reached. But with the exception of Synfuels Corp. Chairman Edward E. Noble, no one in the administration seems enthusiastic about Great Plains.

"We were handed a difficult problem: a project that cost $2 billion to build and probably is worth only $1 billion," Corcoran said. "The question is; Who eats that billion dollars?"