President-elect Ronald Reagan yesterday began reviewing staff proposals for controversial spending reductions throughout the domestic budget, from tougher eligibility rules for welfare, food stamp and student loan programs to sharp cutbacks in federal credit programs for housing and rural power development.

The new administration hopes to present its spending and tax proposals to Congress by mid-February and although the two plans will be combined, Reagan aides have been given a clear warning from leaders in Congress and the financial community that there must be action on spending before tax cuts take place.

David Stockman, Reagan's choice as director of Office of Management and Budget, expects that individuals probably would not receive a 1981 tax reduction until July or perhaps later, but he said that does not reflect a downgrading of individual tax cuts in Reagan's economic strategy. Assuming that Congress takes three or four months to pass a 1981 tax bill, it would then require several months more to change the withholding schedules for individual taxpayers, and only then would the effect of the tax cut appear on paychecks, Stockman said.

Reagan aides are concentrating on cuts in spending and budget authority in the 1982 fiscal-year budget and once programs have been targeted there, they expect to work backward, trimming as much as possible from these programs in the current fiscal year.

The political counterattack has already begun in advance of any final decision by Reagan on spending cuts. Jerry Wurf, president of the American Federation of State, County and Municipal Employees, said in a speech yesterday that "it would be a disgrace if the Reagan administration tried to lauch its anti-inflation program by cutting federal spending for social programs such as foods stamps, welfare, health care and unemployment compensation at the same time it hands out tax breaks to corporations, oil companies and the wealthy."

Budget proposals by Reagan aides include:

More stringent eligibility standards for a number of individual benefit programs such as food stamps, Medicaid and Aid to Families with Dependent Children -- the principal welfare program for poor families -- on the theory that current rules allow benefits to go to those who are not truly needy.

The specific changes in elgibility rules under consideration haven't been disclosed.One likely approach would be to restrict the amount of money a low-income, working parent can earn and still qualify for AFDC or food stamp assistance, said congressional aaides who have worked with the Reagan transition staff. AFDC recipients can deduct work-related expenses such as transportation and tools in determining whether their income is below the eligibility ceiling, and this deduction could be standardized.

Limits on extended unemployment benefits -- 13 weeks of additional unemployment aid that becomes available when the national unemployment rate reaches 4.5 percent. Reagan aides reportedly have been considering raising this trigger point, and changing the program to bar extended payments in states with unemployment rates below the national trigger level on the ground that providing extended jobless benefits in these states make unemploymed persons less likely to seek available jobs.

A broad campaign to restrict the credit activities of the federal government, which, in Stockman's view, constitute an open checkbook that helps finance or support many activities beyond the direct control of Congress or the administration.

The Reagan staff is focusing in particular on the Federal Financing Bank, created in 1974 to centralize borrowing activities by a number of federal agencies. Borrowing by the FFB hs grown rapidly, from $14.5 billion in fiscal 1980 to an estimated $23 billion in the current fiscal year, as, for example, it increased its purchase of disaster loans issued by the Farmers home Administration. The Obigations of such federal agencies, once taken over by the Ffb,ultimately are financed by Treasury borrowing, adding to the government's demand for credit.

Reagan aides would eventually like to cut FFB borrowing in half. For example, they would like to limit loan and credit activities involving the Farmers Home Administration, the Tennessee Valley Authority, low-income public housing, mass transit funding, and the Rural Electrification Administration.