The Reagan administration is set to launch its new and politically risky assault on the 1982 budget as early as next week, right after Congress returns to Washington.

The new attack on federal spending, which is likely to dominate the capital's agenda in the weeks ahead, will include further reductions in the federal work force and almost certainly some cuts in the previously sacrosanct defense budget. It will also seek cuts in some non-defense programs that Congress thought it was finished cutting during the painful budget reconciliation process earlier this summer.

Budget Director David A. Stockman tipped the administration's hand yesterday in a speech to midwestern governors meeting in Minneapolis. Responding to a question from the governor of South Dakota, Stockman told the governors, "Within a week, we are going to announce some changes in federal employment levels and agency termination levels that will warm your hearts, even in the middle of winter in South Dakota."

Informed sources in Washington said these personnel cuts would be part of a new package of budget reductions that the adminstration now recognizes are necessary to control the fiscal 1982 budget deficit.

The administration has promised a $42 billion deficit next year, but private economists generally agree that it will be much higher, some predicting that it could reach $100 billion.

The anticipation of bigger-than-predicted deficits is a principal factor depressing investor confidence on Wall Street, driving stock prices lower and interest rates higher in recent days. Persistent high interest rates fly in the face of earlier White House predictions, and have created severe economic strain. The new White House cuts almost certainly will have to include the 1982 defense budget, informed sources said, although President Reagan has said he doesn't want to alter the defense program he introduced with considerable flourish earlier this year.

As approved by the House and Senate, the defense program permits the Pentagon to obligate $136 billion for defense programs next year.

However, these figures were based on 1983 and 1984 defense-spending assumptions, which the White House disclosed yesterday must be revised downward. To stay within the new, lower targets for 1983 and 1984 defense spending, officials say, the White House faces an uncomfortable choice:

Either it must cut the Pentagon's 1982 obligational authority by $10 to $15 billion, or it will have to take a 1983 budget that is lower than 1982's in terms of budget authority. Officials say this second option would undermine the administration's effort to demonstrate its resolve by steadily increasing its defense budgets.

The military services are fighting to prevent any new cuts, informed sources said. Their first tactic has been to tell the Pentagon's civilian leadership that new cuts will force elimination of important programs, whereas civilian budget experts argue that waste and inefficiency can be eliminated.

The Army, for example, is contending that the cuts the White House seems inclined to make would force it to "dis-establish" two combat brigades in West Germany and a division in California. Government budget experts call this a bluff, which they describe as offering up "gold watches" to try to discourage budget cutting.

Cutting the 1982 defense budget will make it politically easier to seek new and politically painful cuts in non-defense programs, according to several administration sources.

They reckon that a willingness to modify the president's $1.6 trillion five-year defense program would show that the new economic situation really is serious, requiring both military and civilian cuts beyond those already approved.

One source noted that Sen. Mark O. Hatfield (R-Ore.), chairman of the Senate Appropriations Committee and a key figure in the administration's effort to win further budget reductions in the still-incomplete appropriations process, will be more inclined to help if the defense budget is reduced.

The appropriations process now offers the only practical vehicle for new budget cuts. Theoretically, all 13 of the appropriations bills should be passed by Sept. 30, when the fiscal year ends.

In fact, though, this is impossible, since Congress doesn't reconvene until next week, and none of the 13 bills has been approved. So a continuing resolution will have to be passed authorizing government agencies to continue spending money pending final action on their fiscal 1982 budgets.

A continuing resolution can authorize spending at current levels, or at modified ones. In the resolution the the White House could try to impose spending levels even lower than those approved in the budget reconciliation package passed in July, and then seek to put those lower levels into law as each of the appropriations bills is enacted.

On the other hand, Congress may feel it has cut enough and refuse to go along with deeper reductions. That could set up a confrontation with Reagan, and perhaps a further undermining of investor confidence on Wall Street, if the president loses.

If Congress fails to make further cuts, it will also diminish Reagan's chances of balancing the budget by 1984.