Today, the first day of the government's new year, the Reagan administration's budget cuts begin to slice the edge off a vast network of domestic spending programs.

Oct. 1--the effective date for most of the $35 billion in cuts--marks the reversal, at least temporarily, of two great waves of government intervention, the New Deal and the Great Society. Instead, the United States now embarks on a policy of withdrawing government benefits from persons making from $6,500 to $17,000 a year, an income class making up well over 30 percent of the population and including the working poor.

They are people like Barbara Fanning, a $460-a-month part-time crossing guard in Nashville. She has already been notified that she will lose a small monthly welfare payment, which is a minor deprivation. But with it will go, or at least be curtailed, the full Medicaid coverage she and her asthmatic 8-year-old son currently depend upon. Fanning, 30, is typical of many of those who will be hit first by the Reagan administration budget cuts--families run by women, most often with some form of earnings.

For state and local governments that depend on the federal government for one-quarter of their revenues, the cuts are now being translated into a reality that differs from jurisdiction to jurisdiction. As states struggle to sort out the fiscal consequences of both the federal budget and tax cuts, they have already raised taxes by $2.5 billion, and many legislatures are still to hold special sessions.

The state of Arizona expects to be hurt less severely by the budget cuts than many others. "We already run very conservative programs," said Don Mathes, of the Department of Economic Security. Still, the director of the Arizona department's volunteer services division, said, "We are putting all our front-line people through a violent incident training program showing them what to do when some of these people show up at the worker's desk. We expect a little stress in the office."

At the same time, the first of three individual tax rate cuts starts today. For a family with two children and a $10,000 income from a single wage-earner, the total reduction over three months will be $4.68 on federal taxes of $374. The $100,000 family with a single earner and two children would get a $348 reduction on taxes of $27,878. Corporate reductions have already gone into effect, along with a retroactive reduction in capital gains taxes, a step designed to encourage investment by the wealthy.

The spending cuts have hit unevenly. About 270,000 public service workers have already been let go and school lunches almost everywhere have gone up by 20 to 30 cents. A scattering of school systems have dropped out of the subsidized program altogether.

Most users of the college student loan program appear to have beaten tighter regulations by getting applications in before today. This will postpone an expected outcry until the start of the school year in 1982, just the time congressional election fights will be heating up.

Over the next three months, however, as regulations are put into place, is the period when people with marginal incomes--office building cleaners, waitresses, part-time beauticians, maids, crab pickers and chicken pluckers--will see the elimination or reduction of partial welfare benefits, Medicaid health coverage and food stamps.

The scope of the changes is reflected in the following rough administration and congressional estimates: in the Aid to Families with Dependent Children program, the basic welfare program, 400,836 families will be cut off the rolls and another 258,528 will have benefits reduced. In the food stamp program, 875,000 families will be dropped from the program and 1.4 million households, or 5 million people, will have benefits reduced.

The 22.5 million people who have been eligible for health care through the Medicaid program face changes that will vary from state to state, but the final outcome is likely to be determined at one level by the competing lobbying strength of the poor, the elderly, the disabled and the blind, and at another by political competition between hospital, doctor, nursing home and pharmaceutical interests.

Changes in the unemployment compensation program will mean 1,055,000 civilian workers who would have been eligible for extended benefits under the old law will not be during the fiscal year starting today. About 130,000 servicemen and women who voluntarily leave the military will no longer be eligible for unemployment benefits.

The cutback of the trade adjustment assistance program providing benefits to U.S. employes put out of work because of foreign competition will mean a loss of benefits for 234,000 persons this fiscal year. The phasing out of the public service section of the Comprehensive Employment and Training Act has resulted in the elimination of 314,000 job slots.

The administration contends that, in the main, the cuts in these programs are designed to speed achievement of a balanced budget by 1984 and to reduce an economically unproductive dependency on government programs.

The specific economics of the budget cuts are illustrated by the case of Connie Wilson, 36, of Sioux City, Iowa, who earns $722 a month at the local Community Action Agency. Her oldest son works after school in a sports store and makes $120 a month. The mother of five children, she has, until now, also qualified for a $481 monthly payment from the Aid to Families with Dependent Children program, which made her eligible for Medicaid.

Effective today, however, she loses both the welfare and Medicaid coverage if she and her son keep their jobs. If she chooses to quit her job, she would qualify for a $516 monthly welfare payment, an amount roughly equal to or exceeding her family's actual take home income after expenses. Or her son could quit work and the family would qualify for a smaller welfare payment. With the welfare payment, however, would come a return to the Medicaid program with full medical coverage and eligibility to receive up to $250 in food stamp benefits.

By any strict accounting standard, it is to her advantage to quit work and go on welfare, a choice she does not, in fact, intend to make.

The administration has initiated a government-wide effort to ease the regulatory burden on American business, an effort to allow companies to fully exercise competitive instincts and business acumen for expanded growth and production.

In direct contrast, for the food stamp recipient, welfare beneficiary and applicant for free or reduced-price school lunch, the regulatory apparatus has been expanded. Applications for school lunch subsidies will have to include the parents' Social Security number and a pay stub or other form to verify income claims.

Welfare workers are to inspect clients' homes to determine whether they violate the lowered ceiling on assets from $2,000 to $1,000 and make detailed dollar value judgments on lists of goods that fall within the asset category. Food stamp and welfare recipients are to submit monthly income reports, as opposed to the general current practice of periodic accounting.

In the case of welfare and Medicaid recipient Fanning, the administration effort to force increased work and productivity translates into a cutoff of benefits. By contrast, for unprofitable companies like Ford Motor Co., International Harvester and Chrysler, the administration won passage of a new tax provision that effectively amounts to an indirect tax subsidy from the federal government to the corporations in return for new investments.

By rewriting the tax law governing leasing, the government has allowed profitless companies to lease, instead of buy, new investments from profitable companies. It is a new kind of transaction that allows the poor company to sell for cash previously useless investment tax credits.

A state-by-state survey by Washington Post special correspondents reveals great disparities in the impact of the cuts.

In Vermont, Gov. Richard Snelling, an early supporter of the Reagan program and head of the National Governors Conference, now complains that the cuts were "too much, too fast," and the disruption they are likely to cause may severely wound, if not dismantle, the drive toward austerity.

The political consequences of the cuts will largely depend on the success or failure of the entire Reagan economic recovery program. Iowa, in a matter of just two elections, changed from having two of the most liberal Democratic senators in the country, John Culver and Dick Clark, to two of the most conservative Republicans, Roger W. Jepsen and Charles E. Grassley. Without a marked improvement in the economy, Jepsen and Grassley face the prospect of explaining to the families of an estimated 9,600 students, most of them middle class and key swing voters, why they are going to have their student loans cut off next year.

Similarly, Iowa farmers will face a cutoff of $90 million in lending by the Farmers Home Administration and other rural lending agencies that will affect, according to local estimates, up to 2,150 households, not to mention the effects the reductions in commodity supports contained in the farm bill still before Congress will have on farmers' income.

Parallel consequences in nearby Kansas are probably a factor in the recent calls by Sens. Robert J. Dole and Nancy Kassebaum, both Republicans, for shifting more of the new budget cuts to the Defense Department.

It is not at all clear yet how cuts in federal subsidies of the school lunch program will affect farming, but, with prices for students from families of four with incomes ranging from $8,450 to $15,630 doubling from 20 cents to 40 cents, and the price for those from higher-income families jumping from about 60 cents to 80 cents (in some cases rising to $1 or $1.25), school officials report a decline in student participation, ranging up to a 25 percent dropout rate in Rhode Island.

In theory, poor children--those from families with income less than $8,450--are to continue to receive full access to free school lunches, but a small percentage of schools in scattered districts are dropping out of the national program altogether.

In Arizona, at least seven districts, including the Paradise Valley district with 19,072 students, 1,630 of whom qualify for free or reduced-price lunches, have withdrawn from the national school lunch program. In Pulaski County, Ark., the junior and senior high schools, with just over 14,000 students of whom 3,700 are eligible for reduced-price or free lunches, have withdrawn.

Although the sharpest cuts are concentrated on the working poor, the farm program reductions, school lunch and student loans, among others, are progressively to be felt among middle class (and more Republican) voters. At the end of this year, one cut will be felt by all the elderly: the deductible amount of hospital costs that the recipient must pay will increase by 27 percent, from $204 to $260.

In addition, the Comprehensive Employment and Training Act cuts are already being felt in some basic public services. In Cowlitz County, Wash., for example, the CETA program paid for workers to staff the community's only library service, a bookmobile. Cancellation of the CETA program forced voters in the county to take the issue of continued financing of the bookmobile to referendum. Local firemen, who viewed the spending proposal as a threat to continued financing of their work, successfully fought the expenditure, defeating it by a vote of 1,526 to 1,153 on Sept. 15.

Similarly, a fiscally fragile bus system in Athens, Ohio, collapsed last month when CETA funding of the bus drivers' salaries was canceled.

The new economics of scarcity, and the political pressures that follow, are exemplified in Arkansas, where Frank White, the state's second Republican governor in more than a century, decided to deepen cuts in the basic welfare program by shifting money from AFDC to the Medicaid program. The basic monthly AFDC grant for a family of two will drop from $133 to $100 and for a family of nine from $304 to $229.

The governor's decision has prompted complaints from some Democrats that the state administration yielded to pressure from the nursing home lobby--which gets a significant share of the Medicaid program--at the expense of welfare recipients. Children, said Democratic state Rep. Don McKissick, of Star City, "don't have a very strong lobby."

In Texas, the federal cuts in unemployment benefits are not as severe as the actions adopted by the state legislature, which voted to prohibit benefits for those who quit their jobs, are fired for cause, or refuse to take "suitable" job offers.

In addition, a largely unnoticed provision in the food stamp cuts prohibiting stamps for persons on strike is likely to have a significant effect on labor-management relations. In West Virginia, for example, the families of 27,000 striking mineworkers received food stamps during the 72-day walkout earlier this year.

States and cities report widely varying results in efforts to place fired CETA workers in jobs in the private sector. South Carolina officials claim to have placed 76 percent of those let go. But in Dade County, Fla., officials set up a program called Project Hire to place 2,650 laid-off workers, but only 100 were hired by private companies. Graphics 1: chart - Administration figures on state by state numbers of families being cut from rolls or facing reductions in their benefits under Aid to Families with Dependent children. Graphics 2: chart - Chart details cutback in federal government funds for such things as day care centers, special hospital services, child abuse programs and other basic social services. Contributors

The following Washington Post reporters and special correspondents contributed to this report:

Alabama: J.M. McFadden; Alaska: George R. Spivey; Arizona: Al Senia; Arkansas: Bill Rutherford; California: Jay Mathews; Colorado: Joe Seldner; Connecticut: George Judson; Delaware: Sharon Fitzger