The U.S. Tax Court, which hears tax disputes, and the Federal Labor Relations Authority, which resolves labor disputes involving federal workers, both say they will be forced to shut down for a month or more unless their budgets are increased.

The Committee for the Purchase from the Blind and Other Severely Handicapped, which decides what products the government will buy from handicapped workers, doesn't have enough money in its budget to call a board meeting.

And the Administrative Conference of the United States, which recommends ways to make government agencies more efficient, doesn't have enough money to fill a senior executive vacancy.

All of these agencies and about 10 others have been caught in a double budget crunch since December, when President Reagan and Congress approved a continuing resolution that called for a 4 percent across-the-board budget cut. But that budget cut was based on the funding level of the lower of the appropriations bills that the House and Senate had passed for each agency. And for agencies where one chamber had accepted President Reagan's earlier call for a 12 percent cut, that added up to a 16 percent cut.

When Congress returns Jan. 25, many of these agencies are preparing to ask Capitol Hill for some sort of relief from the binding resolution that expires March 31.

"A lot of federal agencies are just dying out there," a senior member of the staff of the Senate Budget Committee explained yesterday. "No question about it, they are hurting and they will be putting a lot of pressure on Congress to do something about it."

The agencies that are hurting are covered by the Treasury, Postal Service, and general government appropriations bill. The Senate's lower appropriation, for $9.4 billion, had set a 12 percent cut for the Tax Court, five offices within the Treasury Department, four agencies in the Executive Office of the President, and eight other independent boards, including the Office of Personnel Management, the Merit Systems Protection Board and Federal Labor Relations Authority.

Hardest hit were agencies whose budgets contain mostly fixed expenses, such as salaries.

Charles Casazza, clerk of the Tax Court, said that nearly 90 percent of the court's $12.4 million budget covers fixed costs. "Most of our budget is rent to the General Services Administration , travel for judges to hearings, court reporting costs and salaries for 225 employes. Now you tell me where I can cut that?"

Last year, Casazza said, 31,500 cases were filed at the court and 11,500 are still unresolved. With a backlog of 34,500 cases already, that added up to the biggest backlog in the court's history.

"The cuts couldn't come at a worse time," said Casazza. "I've tried not to panic and not sensationalize this or scare people, but I can say objectively that if the 16 percent cut continues . . . it would be difficult for us to continue hearing cases and stay in operation. We would just have to shut down for a month."

Because the court schedules its hearings 90 days in advance, Casazza said has not been able to react to the December cuts yet. "They Congress will do something," he said. "They've got to."

Others are not as optimistic. Most agencies have cut out all travel, trimmed training programs, ended research grants and are now taking the ultimate steps: furloughing or RIFing employes.

OPM spokesman Pat Korten said the agency will "separate" somewhere between 200 to 300 of its 7,000 employes during the next two months. "I say separate rather than RIF, because many of the spots will be solved through attrition," Korten said. OPM also is considering furloughing another 200 to 300 employes for at least one day a month, he said. The Federal Election Commission has RIFed 16 auditors and is considering RIFing 14 more, a spokesman said.

Charles Fletcher, director of the Committee for the Purchase from the Blind and Other Severely Handicapped, plans to furlough his 12-member staff one day a week for the next three months to raise $6,000 to pay for a bimonthly meeting of the committee's presidentially-appointed board.

"We couldn't afford to fly any of the out-of-town board members to a meeting unless we furloughed people," said Fletcher, whose committee had sought $621,000 for fiscal 1982 but is earmarked for $524,000 under the 16 percent cuts.

James Shepard, executive director of the Federal Labor Relations Authority, said the cuts have reduced his agency to a "skeleton crew" that can barely handle its current crop of cases. "We are doing little new investigation," he said.

The 16 percent cuts ultimately may cost the government money, some agency heads said, because it will take additional funding to catch up for lost work.