Health, Education and Welfare Secretary Joseph A. Califano Jr. sat in his shirtsleeves for 10 hours on a stage yesterday and listened to 60 witnessess tell him how to reform the nation's welfare system.

When Keith W. Daugherty, general director of the Family Service Association of America, said in a self-deprecating way that he had "no grand design" for restructuring the system, Califano fired back good naturedly, "You're one of the few people in the country who don't."

Califano's department is gathering ideas for a welfare restrucuring plan it must submit to President Carter on May 1. Yesterday's hearing, in an HEW auditorium, was part of that process.

The witnesses was mainly from HEW's traditional clients, groups that favor liberalization of the system. Many told Califano the federal government should assume a larger share of welfare costs. Some also said the government should put a federal floor under welfare payments in the states, by promulgating minimum national eligibility criteria and benefit levels. That, too, could be expensive, and Califano asked several witnesses wryly whether they had "any suggestion as to how the federal government shold raise the money."

Carter has said on the one hand that he wants to reform welfare, but he also said he wants to hold down federal spending. The weldare revisions he has said he will send Congress later this year will thus be an interesting early test of his inclinations.

The program that most people mean when they say welfare - and the program the witnesses talked the most about yesterday - is Aid to Families with Department Children, or AFDC. This assistance goes mainly to needy mothers and their children in families where, for one reason or another, the father is no longer in the home.

There are now just over 11 million people aided through this program - one American in every 20 - at an estimated cost in the current fiscal year that will and Sept. 30 of $10.3 billion. The federal government will pay about half of that, state and some local governments the rest.

State and affected local governments are especially anxious that this federal share be increased as a kind of roundabout revenue sharing. Several witnesses yesterday, among them Pennsylvania Gov. Milton J. Shapp and Hyman Frankel, general counsel to New York City's Human Resources Administration, representing Mayor Abraham D. Beame, urged that the federal share be raised to 75 per cent immediately as an interim step. Eventually they want the federal government to pay 100 per cent.

Several witnesses also urged that the government set unspecified minimum eligibility and payment standards. Currently, within very broad federal limits, each state is allowed to determine these things for itself. The result is a patchwork. Mississippi pays its welfare families an average of $47.81 a month, while Wisconsin, highest paying state on the continent, pays $296.79 and Hawaii, $356.75.

Califano kept asking witnesses what they thought of having a minimim federal differentials to adjust for differences in costs of living. it sounded as if he likes that idea.

Other aspects of the system were also critized the hearing. Catherine Day-Jermany, representing the National Organization for Women, complained that welfare's work rules make no sense. The rules put pressure on welfare mothers to work, but other HEW rules, she said, say that foster mothers may not work and must stay home with their foster children.

The departments plans to hold other public hearings in its administrative regions around the country in the next several weeks. The welfare plan is being drafted under the supervision of assistant Secretary-designate Henry Aaron, formerly of the Vrookings Institution.