Democratic presidential hopeful Walter F. Mondale is careful not to propose vast new social programs. But he argues that President Reagan's philosophy of hard work and self-reliance fails to take account of millions who ''need a little help once in a while.''

If elected, Mr. Mondale would restore many of the cuts made by Mr. Reagan in nutrition programs, social service, housing assistance, and other programs. He does not say that all the Reagan cuts were wrong but simply that there should be greater equity in bearing the burden of reducing the budget deficit.

The basic Democratic argument is that it is the poorest segments of society, who have no political clout, on whom the Reagan spending ax fell most heavily and unfairly.

Thus, all entitlements make up about one-half of thefederal budget but only one-fifth of those entitlements is for means-tested programs, including food stamps and aid to families with dependent children. Yet, according to the nonpartisan Congressional Budget Office, more than half of the Reagan cuts have come from that portion of the budget targeted on low-income people. Moreover, unlike the benefits for the middle class, including social security, most welfare payments and benefits for the poor are not indexed for inflation. So the poor and needy have been disproportionately hurt.

Mondale says it is due to the spending cuts as well as the recent recession that poverty is on the rise in the United States. According to the Census Bureau, the number of poor has risen by almost 900,000, from 34.4 million in 1982 to 35.3 million last year. The poverty rate is especially high for blacks and Hispanics. Some 5.3 million children under the age of 6 were living in poverty last year, or 1 out of 4 children in that age group.

With a view to improving fairness as well as enhancing competitiveness in American life, Mondale has proposed a deficit-reduction plan that calls for $30 billion in social spending as well as a tax increase that favors families earning less than $25,000. Indexation of income taxes for inflation would be deferred or modified for families making more than that. Also, only the first $ 60,000 in adjusted gross income for a married couple and the first $45,000 in adjusted gross income for single persons would be eligible for the final 10 percent of the Reagan three-year tax cut.

Mondale stresses helping the poor by improving opportunities for them. For instance, a share of the proposed $30 billion in social spending would be used for job training.

Another $11 billion would go toward improving quality of schools, helping disadvantaged children, and upgrading basic research. And, while Reagan stresses the responsibility of parents and students to pay for higher education, Mondale calls for an additional $1.5 billion for college student aid. Reagan proposals would have required graduate students to take out loans at higher interest rates; Mondale would establish new fellowships for outstanding graduate students.

Mondale says new tax revenue would be put in a special trust earmarked for reducing the deficit. The $30 billion in new social spending would come from cuts in defense, health costs, farm subsidies, and nonentitlement programs.

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