The president's Office of Management and Budget has ordered major reductions in agency budget requests for key Democratic social programs -- holding them below what is needed to offset inflation or, in some cases, under this year's spending levels.

The cutbacks include a proposed $2.6 billion reduction in the Labor Department's request for continuing federal job programs as well as sizable and transportation programs. There are virtually no new initiatives.

However, such major programs as Medicare, Social Security and food stamps, which by law must provide benefits to anyone who meets eligibility standards, are likely to grow with inflation.

The OMB orders, designed to meet President Carter's pledge to keep the fiscal 1980 budget deficit below $30 billion, represent an initial ruling and are being appealed to Carter personally by the agencies involved. The deadline for appeal is late tomorrow.

However, key adminstration officials say the president is likely to hold firm on virtually all the OMB-imposed ceilings and probably will insist that agencies make new cuts in other areas if they want to see restoration of the money that OMB cut.

The cutbacks involving the job programs would slash spending under the Comprehensive Employment and Training Act program to $8.2 billion, or $2.6 billion below this year's levels. The move would cut job levels in one part of the program by twothirds to 267,000 slots.

Budget makers also want to trim spending for youth employment programs to $882 million, from $930 million this year, Job slots created as part of this year's anti-recession program would be eliminated.

But there are other cuts:

The Department of Health, Education and Welfare has been ordered to hold spending to $196.2 billion, some $2 billion less than it asked for and $6 billion below what it would need to keep up with inflation. Among those programs affected would be federal aid to education, major government health programs and the research and operations of the National Institutes of Health. NIH would get $2.96 billion, down from $3.12 billion this year.

The new federal Energy Department was told to hold its operating budget to $8.8 billion, rather than the $10.5 billion the department requested beyond one-time start up costs with substantial cuts research on coal gasification and oil shale. Among the major reductions are key breeder reactor and nuclear fusion programs and construction of a solvent refined coal plant designed to deal with pollution problems. However, OMB did allow some increases in solar energy research.

Federal transportation programs would be held below this year's level of $19 billion, with no increases to cover inflation, if OMB officials have their way. The cutbacks are spread throughout most of the Transportation Department's programs.

Budget officials also report scores of smaller cuts throughout all major departments and agencies. For example, the Justice Department lost a bid to beef up the U.S. Border Patrol as part of an effort to stop the entry of illegal aliens.

Officials say there also will be some cuts in agricultural programs, although neither the food stamp program nor farm commodity programs are likely to be affected. And Carter is planning to abolish the U.S. Travel Service, which is designed to attract travelers to this country.

One of the major unresolved issues is the defense budget, Carter originally planned to boost the Pentagon budget by 3 percent above inflation, but the White House has hinted he may be reconsidering after liberals complained the military budget should not be exempt.

The 3 percent increase was in line with a pledge Carter made last year at a meeting of the North Atlantic Treaty Organization. However, officials now are pointing out that the promise was made contingent on economic circumstances, and inflation -- and the need to control the budget -- is more critical now than it was in 1977. Carter began work on the defense budget yesterday.

The budget-cutting has drawn predictable protests from agency officials. "There were some ashen faces around here after OMB got through," one department budget official said. "They weren't kidding around this time."

The decisions were made by OMB officials, with ultimate approval by budget director James T. McIntyre. Carter gave McIntyre full authority to propose cuts on his own this time, deciding not to enter the budget process himself until the appeal stage.

The new budget, to cover the federal fiscal year that begins next Oct. 1, is expected to be made public late next month. The budget deficit for fiscal 1979, the current fiscal year, is estimated to run at about $39 billion.