The Reagan administration's budget cutters have selected popular federal spending programs for deep cuts or total elimination during the next four years -- cuts that are likely to provoke serious political opposition in Congress.

According to authoritative sources in the administration and on Capitol Hill, the administration has targeted not only obvious candidates like public service jobs, Medicaid and food stamps, but also some sacred congressional cows like the Farmers Home Administration, the Tennessee Valley Authority, the National Endowments for the Arts and Humanities and child nutrition programs.

The White House hopes to all but eliminate trade adjustment assistance, a program that began modestly in the mid-1970s to help workers deemed to have lost their jobs because of competition from imported goods, which has now burgeoned into a $3-billion-per-year enterprise. The administration also hopes to make major reductions -- as much as 40 percent of total costs -- in standard unemployment benefits.

Cuts like these, which affect poorer Americans, will be politically offset by reductions in benefits to the wealthy and to business, these sources said. For example, the administration hopes to reduce substantially the lending authority of the Export-Import Bank, which finances American exports, principally those of big corporations.

However, the proposed cuts that have been disclosed so far would be significantly harsher for lower-income groups than for the well-off. Specific details of cuts proposed by the new administration's Office of Management and Budget were published yesterday in the Chicago Sun-Times, which said it had acquired a copy of a memorandum listing them. Much of the information in the Sun-Times account was confirmed by informed sources yesterday.

What is not clear in the figures now available is the base against which they are to be measured. In some cases, the proposed cuts will be in the 1982 Carter administration budget; in others, they will be based on current operating costs, and in the remainder the cuts will come from long-term authorization measures stretching into the mid-1980s.

A key White House official stressed that there these are just proposals and that President Reagan has not yet finally approved any of them. The proposals emanate from working groups established by David A. Stockman, the director of OMB.

Reagan is scheduled to address the nation on economic matters tomorrow night at 9, and plans to present specific proposals Feb. 18 for cutting the budget.

According to the Sun-Times, OMB's working groups, which include the secretaries of relevant Cabinet departments, include the following targets:

Cutting $2.6 billion out of the food stamps program by fiscal 1982, which begins next Oct. 1. This would be achieved by reducing both benefits and the number of citizens eligible for food stamps by two to three million.

Eliminating most of the Carter administration's huge federal program to encourage new forms of energy or "synthetic fuels," OMB would continue just eight "first of a kind" demonstration plants, cutting out numerous other federally financed enterprises to save tens of billions in the mid- and late 1980s.

Saving $1 billion in fiscal 1981 and $3.7 billion in 1982 by phasing out about 350,000 public service jobs authorized by the Comprehensive Employment and Training Act (CETA).In 1981, the Sun-Times said, OMB proposes a freeze on CETA jobs and then wants to eliminate them in 1982.

Reducing grants given by the National Endowments for the Humanities and the Arts by 50 percent. One White House aide speculated last night, however, that the administration's final proposal would be for smaller cuts in the Endowments.

Reducing Medicaid spending for health care for poor people by $1 billion in 1982 by imposing a cap on federal participation in this program. Under the OMB proposal, it would be left to the states to decide how to adjust to this reduced federal contribution.

Making large cuts in child nutrition programs -- $1 billion by 1982, according to the Sun-Times -- by eliminating some subsidies for snacks in day-care centers and reducing other federal aid for school meals.

Capitol Hill sources revealed yesterday that the Reagan White House plans a radical change in the ability of government agencies to raise money through the Federal Financing Bank. This move would force agencies like the Tennessee Valley Authority and the Rural Electrification Administration to raise money in the private sector at commercial interest rates, instead of at more favorable Treasury bill interest rates.

This change would substantially reduce borrowing by the federal government while increasing borrowing costs to TVA and REA, perhaps by millions of dollars.

Leaks of the cuts that the White House hopes to make in the federal spending are one weapon available to those who will fight these spending reductions when they are formally proposed.

Republican leaders in Congress sympathetic to the White House's budget-cutting intentions said yesterday that prolonged public discussion of proposed cuts before they are introduced would diminish the new administration's chances of ultimate success.

A spokesman for Stockman said last night that he would have no comment on the Sun-Times figures, and added that "every piece of paper" now being produced by OMB should be stamped "draft."