If President Reagan has a major political vulnerability on the domestic front , it is the charge that he is unfair to the poor. The President maintains that he has not done away with the ''safety net'' of social benefits for the ''truly needy.'' He is right, say economists. Because of congressional action, the welfare system remains largely intact. Mr. Reagan has scaled back many programs, including food stamps, housing, family aid, and school lunches. But overall, he has mainly cut the rate of growth in social spending, not the total amount spent.

Furthermore, Reagan enjoyed broad public support for his assault on welfare spending. Even Democrats acknowledge that the time had come to put a break on the New Deal and Great Society splurge and try to make government programs more effective.

However, studies show that under the Reagan presidency the gap between the rich and poor has widened. The administration's tax and spending cuts have benefited mostly wealthy families while the poor have suffered. The Urban Institute, a nonpartisan public policy research group, found that since 1980 the disposable income of the richest one-fifth has risen by 8.7 percent, after inflation. Middle-income families are only slightly better off. The income of the poorest one-fifth of families has declined by 7.6 pecent.

The working poor have been especially hard hit because welfare benefits now go essentially only to those who cannot work. But a Princeton University study indicates that most working poor, faced with losing their benefits because they are earning above the permitted income ceiling, choose to work rather than put themselves entirely on welfare. This suggests, the researchers say, that the Reagan policies may be breaking the spiral of dependency on welfare.

Reagan does not deny that many poor are experiencing hardship. But he maintains that sturdy economic growth will generate more and more jobs, helping all segments of society. He also argues that the decline in inflation helps the poor significantly because low-income families spend the bulk of their earnings on necessities.

Also, as a matter of philosophy, Reagan does not believe it is government's task to narrow the gap between the wealthy and the poor by equalizing income. Sensitive to the ''fairness'' charge, Reagan vows he will raise taxes in a second term only as a ''last resort.'' He also promises he will not reduce social security benefits for those receiving them now or expecting to receive them in the future. The elderly have in fact done well in the past four years, largely because of cost-of-living adjustments, abnormally high real interest rates on their savings, lower inflation, and lower taxes.

In Reagan's eyes, ''fairness'' also extends to such issues as tuition-tax credits for parents sending their children to parochial and other private schools. The President argues that it is unfair for parents sending their children to private schools to pay taxes for a public school system they do not use and not to receive any relief for private tuition costs.

Critics, including Democratic challenger Walter F. Mondale, counter that the passage of tuition-tax credits would undermine the public school system, so essential to a working democracy, and add billions of dollars to the budget deficits.

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