The social security system's fate is back in its familiar position as a hot political issue. President Reagan and Democratic candidate Walter Mondale sparred on the subject of who did what to social security in the past, during their debate Sunday.
The political slugfest continued Tuesday when Mr. Mondale charged that Mr. Reagan had a ''secret plan'' to cut benefits after the election. The President responded by expanding the pledge he made in the debate to protect benefits paid to 36 million current beneficiaries.
The administration's updated policy is that the ''President will never stand for a reduction of social security benefits for anybody,'' including future recipients, spokesman Larry Speakes said. Treasury Secretary Donald T. Regan charged Wednesday that Mondale is frightening older Americans ''just for cheap political advantage.''
The issue's sensitivity was underscored Tuesday, when President Reagan signed , without the usual public ceremony, a bill making it easier for individuals to claim social security disability benefits and harder to lose them. Administration efforts to curb abuses in the disability program met with criticism when about 500,000 individuals were told they would lose benefits. Some 200,000 were reinstated after appealing.
The controversial nature of the social security system was evident in Sunday's debate, when both candidates made statements about social security's history that were questioned by impartial sources. For example, Mondale appears to have overstated the depth of the cuts President Reagan proposed for the social security program in 1981.
Mr. Reagan, in turn, appears to have overstated the effect of the reductions in future benefits resulting from social security legislation passed in 1977 during the Carter-Mondale administration. That law also included major social security tax increases.
While elements of social security's history are controversial, its present and future look relatively strong, experts say.
Unless there is a very severe recession in the near term, ''there is a very high probability'' that social security ''will not have another financing crisis in the 1980s and also very likely for the following two decades at least,'' Robert J. Myers, executive director of the National Commission on Social Security Reform, recently told Congress's Joint Economic Committee.
Medicare, the health insurance portion of the social security system, does face financial problems due to high health-care costs and the aging of the population. The problems are projected for ''somewhere in the 1990s,'' says a congressional expert on the system who asked not to be named.
Workers may have to increase their contributions to the medicare system ''if we don't get the costs under control,'' Secretary Regan said Wednesday.
In the debate Mondale charged that the President ''proposed to cut social security benefits by 25 percent'' in 1981.
The President did propose cuts that year in the social security program to cope with the looming funding crisis Congress finally acted on in 1983. Some changes, including elimination of the mimimum social security benefit of $122 a month, were contained in Reagan's March budget package. The minimum benefit goes to workers whose earnings otherwise would have qualified them for less.
In a separate social security package unveiled in May, Reagan proposed other changes in the system, including reductions in early-retirement benefits and in disability benefits. The plan was greeted with strong criticism from Democrats and lukewarm support from Republicans, and only selected elements were enacted.
The overall package was estimated to save $81.9 billion over the five fiscal years ending in 1986. Since social security payments during that period were projected at $901 billion, the proposed reductions were less than 10 percent.
Proposed reductions in specific programs, however, were larger. Payments to those who retired at age 62 would have been chopped from 80 percent of the age- 65 benefit to 55 percent of the normal retirement payment. That would have been a 31-percent reduction.
While Mondale overstated Reagan's proposed cuts, Reagan also exaggerated benefit reductions passed in 1977 when he said: ''The only 25 percent cut that I know of was accompanying that huge 1977 tax increase....''
In 1977 Congress did vote phased increases in social security tax rates and in the amount of wages on which taxes were paid, designed to raise a total of $ 227 billion over the next decade.
The 1977 law also corrected, for those born after 1916, a benefit formula that had overcompensated retirees for inflation.
As a result, those who retired at age 65 in 1982, and were entitled to the maximum benefit, received a check 16.3 percent smaller than an individual with the same earnings history who retired at age 65 in 1981, congressional sources say.
The reductions in retirement checks could grow to the 25 percent Reagan cited , ''depending on what assumptions you make about future inflation and wage growth,'' the congressional expert said.