In the six weeks until President Reagan submits his fiscal 1987 budget, the news media will be full of stories detailing administration "plans" to make huge cuts in the government's domestic programs.

Many of these stories have already appeared: The president may seek to cut Medicare and Medicaid by $8 billion; he may propose selling the Federal Housing Administration and other public agencies to private business; he will seek cuts in housing and aid to cities, in urban-transit funds, an end of subsidies to Amtrak; he wants to eliminate aid to Washington's Metro rail system; he wants deep funding cuts at the National Institutes of Health.

When the budget is submitted Feb. 3, most of these stories will turn out to be "true" -- the Reagan budget will indeed call for unprecedented cuts in federal programs. It must.

But none of the president's proposals will take effect without congressional approval, and Congress has shown no appetite for the sort of sweeping changes he is expected to propose. Presidential budgets containing such cuts have been declared "dead on arrival" in Congress for the last several years. So many of the most dramatic leaks that can be expected in the next six weeks are unlikely to become official policy.

The White House is committed to producing a budget that meets the new deficit-reducing targets of the Gramm-Rudman-Hollings law.

It calls for cutting the fiscal 1987 deficit to $144 billion. The White House has estimated that, without new reductions, the anticipated deficit will be $195 billion. That will mean cuts of $50 billion for fiscal 1987.

At the same time, the White House has promised not to cut defense spending in the new budget, and Reagan remains adamantly opposed to tax increases. So domestic programs must absorb all of the cuts he proposes.

Within the domestic cuts, the president will pursue his desire to "thin out" the general level of services provided by government, dismantling programs he feels could be handled better by the states, localities and private sector.

The same philosophy lay behind budgets introduced during his first five years in office, all of them drafted by David A. Stockman, Reagan's first director of the Office of Management and Budget. Stockman has left government, but all of his plans remain in OMB files and will be trotted out again in the new budget.

Under these conditions, the carnage to be proposed by the president for domestic programs could be extremely heavy. He would propose large cuts in Medicare, "privatization" of several federal agencies such as the FHA and federal power-marketing affiliates like the Bonneville Power Administration, and elimination of many functions altogether.

In past years, he has called for elimination of the Small Business Administration and the health-planning program, elimination of the Community Services block grant and the work incentive program for welfare clients, and cuts in student aid and urban aid.

He has also proposed eliminating the Job Corps, cuts in child-nutrition programs, a freeze on many other social programs, a reduction in the federal work force and eliminating more than $200 million a year in training funds for the health professions.

It is virtually certain that his fiscal 1987 budget will again call for these cuts and more.

Congress has been fighting off similar cuts and gnawing away at the Defense Department budget for several years, and the prospect is for more warfare. But the president may well believe that, under pressure to meet the $144 billion deficit ceiling, Congress may accept some domestic cuts that it had rejected.

The $144 billion deficit ceiling is likely to make the infighting more fierce. In the past, there was no absolute ceiling, and everyone could yield a bit here and there to get a final compromise. No more.

The battle will be over how much of his proposals Reagan can get through. The more domestic cuts, the less damage to the Pentagon, and vice versa.

Senate Finance Committee Chairman Bob Packwood (R-Ore.) told the Senate when the Gramm-Rudman-Hollings bill was being cleared that, to reach the 1987 target while increasing defense and avoiding a tax increase, the president "may propose termination of 30 to 50 domestic programs costing, on average, about $1 billion apiece."

Packwood said, "Congress has from February to September to change the president's priorities . . . .

"If we do not want to terminate 30 to 50 social programs, we do not have to. We can take it out of defense.

"If we do not want to do that, we can pass a tax increase. When I say we can do this or that, I recognize that we are not unfettered in this. Any law has to be passed by both houses of Congress and signed by the president. If he does not sign it, it does not become law."

The Gramm-Rudman-Hollings act exempts some huge government programs from arbitrary cuts and strictly limits possible cuts in others. Social Security, the single biggest program, is totally exempted, and health-care programs are heavily protected. Most "welfare" programs that help the poor are also protected.

But this legal protection need not apply to Reagan's budget. He can offer cuts in any program and try to have Congress adopt them. Only if he and Congress fail to find $50 billion in cuts voluntarily will the automatic cuts required by Gramm-Rudman-Hollings take effect.

Given this freedom to propose anything he chooses in his initial budget presentation for fiscal 1987, the president will follow his priorities and hope that he can push his budget plan through Congress, before the start of fiscal 1987, thus reaching the $144 billion target without resorting to the automatic procedure.

If Congress and the executive fail to agree on voluntary cuts to meet the goal, the automatic procedure will take equal amounts from the Pentagon and domestic budgets, without touching the protected programs. This could mean a $25 billion cut in the Pentagon budget, something Reagan can be expected to fight to avoid.

Many in Congress have said they suspect that such a prospect will finally compel the president to accept some kind of tax increase.