The Reagan administration, hoping to avert the possibility of a higher-than-expected 1982 deficit, wants to use the appropriations process to push through spending cuts greater than those mandated in the recent budget bill.

The administration wants the figure to come out closer to the $48 billion in cuts President Reagan asked for in March, rather than the $35 billion mandated by the budget bill.

The larger cuts could help ease a potential budget deficit problem that has emerged recently. While the administration is still sticking to its estimate that the fiscal 1982 budget deficit will be just over $40 billion, congressional budget experts are predicting that the deficit could be nearer $60 billion because of continuing high interest rates, among other factors.

Ed Dale, spokesman for the Office of Management and Budget, said the possibility of a higher deficit "adds urgency" to the goal of achieving the deeper cuts.

When the fight over the budget ended, many members of Congress figured the worst was over and there would be no further cuts for the fiscal year starting Oct. 1.

But the administration has been reminding people in recent days that the program levels set in the budget bill are only ceilings, subject to further cuts in appropriations bills.

OMB's Dale said, "We have always reserved the right to go back and ask for our original figures . . .The general policy, in each case, is that we're sticking by our March budget request."

Although the reconciliation bill imposed program caps or formula changes that will save about $35 billion, it didn't deal with all the appropriations cuts. In some cases it set program figures higher than the administration had sought.

For example, the administration asked $1.4 billion for low-income energy assistance for fiscal 1982 but the budget bill authorized $1.875 billion. It asked $4.4 billion for Export-Import Bank direct loans, but Congress authorized $5.065 billion.

Some departments already are drafting plans to hold their own budgets to the March figures.

Anne Graham, an assistant secretary at the Department of Education, said that her agency proposes to ask Congress to appropriate $13.1 billion for its programs, as it had requested in March, rather than the $15.7 billion that was set as a ceiling in last month's budget reconciliation bill. "Those are our marching orders and we're going to march," she said.

Thus Education will not seek the $3.48 billion authorized in the reconciliation bill for aid to educationally disadvantaged inner-city children. Instead, it will ask for only $2.8 billion, the amount envisioned in March for this program as part of a complicated "block grant" scheme that Congress didn't approve. Similarly, while $1.15 billion was approved for handicapped programs, only the original request of $890 million will be sought.

The House already has passed five of the 13 regular appropriations bills for the year, but many that contain the controversial cut proposals, such as Labor and Health-Human Services, have yet to be considered. The Senate has passed only one major appropriation bill.

President Reagan already has threatened to veto spending bills that are higher than his budget requests. If the appropriations bills get bunched up and Congress decides, as it has before, to lump several into a single "continuing resolution" to keep programs going, a repeat of the first budget strategy is possible.

Administration sources say that a continuing resolution could be a good vehicle for a giant fund-cutting amendment that could be pushed through on one measure. That was how Reagan won on the budget bill.

While OMB was signaling that in general it will hold firm on the deep March cut requests, a House Republican Research Committee unit headed by Rep. William Dannemeyer (Calif.) produced a list of $52 billion in potential cuts above and beyond Reagan's proposals.

The Dannemeyer document, a list of possibilities rather than a hard-and-fast hit list, would wipe out the Office of Technology Assessment, cut salaries and expenses in places like bankruptcy court and district courts, sharply cut foreign aid for such items as training foreign military officials, cut international population planning funds (which it calls "international social engineering") and wipe out special nutrition aid in Puerto Rico.

Also suggested: wiping out tobacco subsidies ("ridiculously ironic in view of anti-smoker ads"), further cuts in food stamps, reduction of outlays for atomic weapons fuel and petroleum reserves, wiping out maritime subsidies, ending federal aid to the National Board for Promotion of Rifle Practice, a major cut in Social Security and other public pensions, using an index that would produce lower cost-of-living increases in benefit programs, elimination of the National Institute of Education ("even Jack Anderson acknowledges horrible waste and fraud in this program"), killing family planning and reducing housing, community development and airport funds.

Rep. Carl Perkins (D-Ky.), chairman of the House Education and Labor Committee and leader of the fight to save education programs from the budget ax, said he didn't think the appropriations committees would go along with the administration's request for further cuts in education. "I don't think they'll cut that deep," he said. "It would just destroy some of our best programs. . . . It would destroy hundreds of thousands of people who will become productive taxpayers. It would pull the rug out from under them."

Terry Herndon, executive director of the 1.7-million-member National Education Association, said yesterday his organization will "strenuously oppose any additional budget cuts for education." He noted that reductions in state and local budgets already have strained school districts' finances.

Rep. Jamie Whitten (D-Miss.), chairman of the House Appropriations Committee, said he was sure his committee would try to hold down overall spending but added, in a reference to administration officials: "After all, we are an equal branch of government. They'll have to expect some differences."

Whitten said he wasn't concerned about the president's hints of vetoes on spending bills he considered too large. "We certainly don't want any showdown here, there and yonder," he said. "We're going to cooperate as fully as we can, but there may be some honest differences."