The Democratic-controlled Congress and the White House yesterday began hurtling toward a collision over the federal budget that some lawmakers predict could ultimately yield "deep and crippling" spending cuts in programs already hobbled during the Reagan era.

Beginning a five-week countdown required by the nation's new balanced-budget law, the Congressional Budget Office yesterday detailed how spending on everything from student loans to AIDS research will be indiscriminately slashed next month if Congress and the Reagan administration cannot find other means of reducing the federal deficit.

The CBO report on the likely impact of $23 billion in across-the-board spending cuts begins what promises to be the final act in the budget-and-tax stalemate that has preoccupied the executive and legislative branches for more than 10 months, an act that may spell defeat for the Democratic strategy of forcing President Reagan to accept a tax increase.

Under the revised Gramm-Rudman-Hollings budget law signed by Reagan last month, agencies will begin to feel the first pinch of the automatic cuts next week when the administration's budget office issues its version of yesterday's CBO report. Spending would be frozen at the levels mandated by the Office of Management and Budget beginning Tuesday and would become final Nov. 20 when OMB files an updated estimate.

The $23 billion cut would be apportioned 50-50 between defense and domestic spending programs, but because of exemptions and special rules only 20 percent of the federal budget is at risk. In most cases, spending would still exceed last year's levels because the base from which the reductions are made is calculated from 1987 appropriation levels plus 4.2 percent inflation and the cost of salary increases.

But compared to what spending would otherwise be with normal growth, the Pentagon would sustain a 10.4 percent reduction and domestic programs would be trimmed by 8.7 percent.

Reagan has decided to exempt military personnel from the cuts, meaning that the brunt would fall on procurement, research and development, and operations and maintenance.

Though the projected $23 billion cut would be far less than the $35.2 billion in spending reductions pushed through Congress in the first year of the Reagan administration, it would be twice the size of the only previous round of automatic reductions, in 1986 under the first version of Gramm-Rudman-Hollings.

Because of Reagan's adamant opposition to a tax increase, many members of Congress predict that the automatic spending reductions -- or at least a scaled-back version of them -- will go into effect.

"The president is absolutely determined to take" the automatic cuts, said Sen. Ernest F. Hollings (D-S.C.).

Though congressional tax-writing committees are drafting tax bills that would raise about half of the $23 billion needed to meet the deficit goal, it is unclear whether a tax bill will pass Congress. And many on Capitol Hill say that overriding a presidential veto of a tax bill would be nearly impossible.

In a defiant statement yesterday, Reagan called the tax plans proposed by House and Senate committees "an exercise in fiscal irresponsibility." He vowed to veto the proposals if they are passed by Congress.

The looming fiscal battles, Sen. J. James Exon (D-Neb.) said this week, will contribute to "the greatest series of confrontations that anyone living today has ever seen between the executive and legislative branch . . . . "

The prospect of across-the-board cuts next month has led this week to a renewal of almost desperate pleas by members of Congress for the Reagan administration to negotiate a budget compromise. It has also brought the first salvos of a campaign to lay the blame at the president's feet if the cuts do occur, an effort that could foreshadow a major political theme in next year's elections.

Touting the $12 billion tax bill just passed by the Ways and Means Committee, for example, House Speaker Jim Wright (D-Tex.) urged the White House "to cooperate with the Congress" in raising taxes in order "to avoid the guillotine" of automatic cuts.

And Senate Budget Committee Chairman Lawton Chiles (D-Fla.) greeted the CBO report with the observation that it could "be the start of the countdown to a major embarrassment . . . or it can mark the opening of the hunting season where Congress and the White House work together to find the savings necessary to reduce the deficit in a responsible way."

Warning of "deep and crippling reductions" in key domestic programs, Chiles asked: "Can it be so hard to find a rational way to find $23 billion in savings out of a $1 trillion budget?"

Absent any changes in spending or tax policies, the CBO projects that the fiscal 1988 deficit would be about $179 billion, approximately $42 billion less than the record high of $221 billion in fiscal 1986, but far above the budget law's original goal of $108 billion.

Edward M. Gramlich, CBO's acting director, told the Senate Budget Committee that because Congress has added another $1 billion in spending this year, the deficit reductions needed to prevent the automatic cuts may be as high as $24.6 billion.

However, the automatic cuts, if triggered, would still total only $23 billion.

The balanced-budget law exempts from the automatic cuts some major entitlement programs such as Social Security, most federal retirement and disability benefits, veterans pensions and some programs for low-income people. Special rules offer limited protection to other areas of the budget, including Medicare and veterans' health programs.

Because the brunt of the cuts falls on discretionary domestic programs that have undergone retrenchment during the Reagan years and because of the large Pentagon buildup over the same period, the reductions would be felt most heavily by traditionally Democratic constituencies.

The anguished cries of some interest groups are being heard on Capitol Hill as lawmakers are urged to protect some of the programs that face the deepest reductions, such as agriculture and education.

Charles B. Saunders Jr., vice president for governmental relations at the American Council of Education, for example, called projections of a nearly $500 million cut in student financial aid "a disaster" that would mean the elimination of aid for most middle-income families.

With the kickoff of the five-week Gramm-Rudman-Hollings season, government agencies across Washington also girded -- with varying degrees of concern -- for the projected cuts.

Here is how some government spending could change if the full $23 billion is cut: Defense: Overall spending authority, which provides for outlays spread over more than one year, would be set at $279 billion. That is $10 billion lower than the smallest amount considered in the congressional budget and $33 billion less than requested by Reagan. In actual outlays for fiscal 1988, the Pentagon would get about $270 billion, about $3 billion less than last year.

Procurement of weapons systems would be particularly hard hit, with a reduction of $9.3 billion in budget authority. Operations and maintenance would be cut by $8.7 billion in budget authority.

Robert W. Helm, the department comptroller, said the cuts in weapons purchase accounts "cannot help but have an impact on efficient procurement from the standpoint of stretch-outs, unit cost increases and things like that." Agriculture: Programs under the Agriculture Department would suffer the largest domestic spending cuts -- about $1.1 billion in outlays -- with only major nutrition programs spared.

The largest dollar cuts would occur in farmers' direct payments, ranging from their income-support subsidies and commodity price-support loans to disaster payments and crop insurance. These cuts could be $750 million in 1988.

Two other USDA agencies that could take heavy hits are the Extension Service and the Agricultural Research Service.

Education: Budget authority for programs under the Department of Education would be cut by $1.4 billion and fiscal 1988 outlays by almost $300 million.

One of the largest cuts, $358 million in budget authority, would come in the Chapter 1 program that provides compensatory education services to disadvantaged children.

In addition, financial assistance for needy college students would be cut by $497 million in budget authority and $93 million in fiscal 1988 outlays, probably lowering awards to more than 1 million students receiving Pell Grants.

"We don't believe the worst-case scenario is likely to occur," said Bruce M. Carnes, deputy undersecretary at the department.

Education groups are more alarmed. Susan Frost, executive director of the Committee for Education Funding, said the projected Chapter 1 cuts would virtually nullify gains made when the program was reauthorized by Congress this year.

Health and Human Services: A broad array of programs, ranging from Indian health to the Centers for Disease Control to the National Institues of Health, would be cut a total of $2.8 billion in outlays for fiscal 1988.

The cuts would have a far-reaching impact not only on hospitals and doctors but on patients. Some patients would have to make up some of the cut, mostly on doctors' bills, out of their pockets.

Medicare payments to doctors and hospitals would be cut 2.3 percent for the remainder of the fiscal year for a total of $1.5 billion.

In addition, the National Institutes of Health would lose about $561 million in budget autority and $261 million in actual outlays. Plans to significantly boost AIDS funding might also be shelved.

Transportation: Programs could lose $2.4 billion in outlays, leaving the department's budget virtually static from last year.

Officials at the department are particularly worried about potential cuts to the Federal Aviation Administration of more than $280 million in outlays.

Cuts at FAA could jeopardize plans to hire 1,000 new air controllers, slow modernization of air traffic control systems and delay local airport improvements.

Cuts to highway aid of $1.2 billion and mass transit of $300 million could delay local projects.

Space and Science: NASA would be cut by about $240 million, affecting not only the space shuttle program but severely curtailing plans to build a space station. "It would be extremely tough on us," said NASA deputy controller Gary Allison. "There's no way we could meet those reductions without major impacts on our programs."

The National Science Foundation would lose $148 million in budget authority, and more than $75 million in actual outlays for fiscal 1988. Interior and Energy: Interior Department programs would lose $446 million in outlays for fiscal 1988. The Energy Department would be cut $839 million.

Although the Interior Department has not done a program-by-program analysis, officials say the impact would be far greater than in 1986.

"This one is going to be more significant," said Joseph W. Gorrell, deputy assistant secretary for policy, budget and administration. Staff writers Molly Moore, Laura Parker, Cass Peterson, Boyce Rensberger, Spencer Rich, Ward Sinclair and Barbara Vobejda and staff researcher Michelle Hall contributed to this report.